
Book iLigJ^. 

Copyright H? 

COPYRIGHT DEPOS1E 



/ 



AN 



• 






, '; 



ELEMENTARY CLASS BOOK 



ON 



ASTRONOMY: 



IN WHICH 



MATHEMATICAL DEMONSTRATIONS ARE OMITTED. 



BY H. N, ROBINSON, A. M. 

FORMERLY PROFESSOR OF MATHEMATICS IN THE UNITED STATES NAVY ; 

AUTHOR OF A TREATISE ON ARITHMETIC, ALGEBRA, GEOMETRY, 

TRIGONOMETRY, SURVEYING, CALCULUS, &C. AC. 




CINCINNATI: 

JACOB ERNST, 112 MAIN STREET 

1857. 



Entered according to act of Congress, in the year 1857, 

By H. N. ROBINSON, 
in the Clerk's Office of the District Court for the Northern District of New York. 



STEREOTYPED BY D. HILLS <fc CO. 
141 MAIN ST., CINCINNATI. 



<b^ 



PREFACE 



Ev£RY one strives to adapt means to ends, and when the author pre- 
pared his large work on Astronomy, he had no other end in view than to 
teach Astronomy to such as may be competent to the task and fully pre- 
pared to learn it. His first aim was to produce a book of the right tone 
and character, without any regard to the number of persons who might be 
prepared to use it. That effort was entirely successful, but the book is not 
adapted to the great mass of pupils, because it requires of the learner 
considerable mathematical knowledge, and a corresponding discipline of 
mind, therefore but few persons, comparatively speaking, feel qualified to 
study that book. At the same time a book of like tone, character, and 
spirit, is demanded by teachers for the use of their more humole pupils, 
except that it must be on a lower mathematical plane, and this book is de- 
signed to supply that demand. 

In this work we have omitted mathematical investigations almost alto- 
gether. Yet we have endeavored to retain the spirit of the University 
edition, and much of the plain matter of fact in that book is the same in 
this. Some of the more abstruse parts of the science are omitted, and 
some of the more simple and elementary parts are more enlarged upon in 
this book, than in that. 

Because we have avoided mathematical investigations, and attempted to 
adapt our work to the common qualifications of pupils, it must not be in- 
ferred that we have therefore made an easy text book, one which requires 

iii 



iv PREFACE. 

no particular attention on the part of the reader to comprehend. Astron- 
omy is no study for children — the subject admits of no careless reading-, 
and however good the book, and however well qualified the teacher, the 
student must take vigorous hold of the study for himself, and, in a mea- 
sure, take his own way to meet with success. 

Although this professes to be but a primary and elementary work, it 
contains more than a mere statement of astronomical facts, it deduces hid- 
den truths from primary observations, and endeavors to draw out the logi- 
cal powers of the reader and make him feel the true spirit of the science. 

Science properly learned is never forgotten, but science committed to 
memory soon evaporates, and science cannot be obtained from books and 
teachers alone, — in addition to the materials, the original perceptions and 
reasoning powers of the learner, must come in with decided earnestness 
and force, — and these remarks are particularly applicable to the science 
of Astronomy. 

We make these remarks to impress on the mind of the teacher the ne- 
cessity of giving perfectly sound instruction, and not be contented with 
memoritor recitations, or the mere accumulation of facts. 

For instance, the sun is nearer to the earth in January than in July, but 
this fact alone is not science, scarcely knowledge — and it would be only 
a dead weight to the mind to crowd it into the memory : but when it is 
ascertained how we know this fact, from what observation it was deduced, 
and what logical induction was applied, then it becomes another matter, 
then it is science, and thus learned, could never be lost. 

Some elementary works on Astronomy put great stress on pictorial illus- 
trations, — but at best such illustrations are little better than caricatures, 
and some of them give incorrect impressions ; for instance, in attempting 
to show the relative motions of the sun and moon in space, by a figure, the 
moon's motion is generally represented as describing loops, when the true 
motion is progressively onward, and at all times concave towards the sun. 



PREFACE. V 

The difficulty of giving true representations on paper, in Astronomy, is so 
great that the teacher should be careful so to guide the perceptions of the 
learner, that they be more truthful and refined than the figure can possibly 
be, or the learner will draw distorted if not erroneous impressions from 
them. For instance, if we wished to make a correct representation of the 
sun, earth, and moon, and made the earth but one-eighth of an inch in. 
diameter, the diameter of the moon's orbit must be 7J^ inches, the diame- 
ter of the moon the 32d part of an inch, the diameter of the earth's orbit 
3000 inches, or 250 feet, and the diameter of the sun must cover 14 inches. 
These considerations show the utter impossibility of making correct as- 
tronomical representations on paper, for who would have the earth drawn 
out less than one-eighth of an inch in diameter, and even that small mag- 
nitude would require a sheet two hundred and fifty feet wide, on which 
none of the exterior planets could be drawn. For these reasons we do not 
place as much value on pictorial representations and astronomical maps as 
many do, and whenever we make use of such things, as we sometimes do, 
we take much care that the impressions drawn from them, are not as gross 
as the representations themselves. 

In conclusion, we would remind the reader that the subject of Astronomy 
is so vast and magnificent, that it is almost as impossible to do justice to 
it in composition as it is in geometrical diagrams. We have made no pre- 
tensions to delineate the high mental satisfaction that a knowledge of 
this science imparts ; we have only attempted to guide others in attaining 
that knowledge, and in this particular we do not claim to have made a 
perfect book, — far from it, — perfection is impossible, decidedly so, when 
applied to a book ; and if all books were perfect, there would be little need 
of schools and teachers. 



CONTENTS 



SECTION I. CHAPTER I. 

Page. 
Introduction 11 

Definition of terms 12 — 17 

CHAPTER II. 

Preliminary observations 18 

The north pole in the heavens — the fixed point 19 

Circumpolar stars 21 

A definite index for the length of years 24 

"Wandering stars 25 

CHAPTER III. 

Pixed stars — landmarks, <fec 26 — 28 

How to find the north star % 29 

How to find any star , 30 — 33 

CHAPTER IV. 

Time — and the measure of time 34 

Sideral time — the only standard measure of time .35 — 36 

Why astronomers commence the day at noon 37 

CHAPTER V. 

Astronomical instruments 38 — 41 

Astronomical refraction 42 — 43 

Effects of refraction 44 

How to find the true altitude of a heavenly body 45 — 46 

How to find the declination of a star 47 — 49 

CHAPTER VI. 

Scientific method of finding stars 50 — 54 

How we may find a particular star 54 — 56 

CHAPTER VII. 

Pixed and moving bodies 57 

Observations showing the motion of the wandering stars 58 

Figure and magnitude of the earth 59 — 63 

Unequal pressure on the earth's surface 64 — 67 

vii 



vin CONTENTS. 



SECTION II. — CHAPTER I. 



First consideration in respect to distance, astronomically speaking, 68 — 70 

Horizontal parallax 71 — 75 

Distance to the moon — deduced from parallax 76 — 78 

CHAPTER II. 

Solar parallax 79 

How to measure the sun's apparent diameter 80 — 83 

Figure of the apparent solar orbit 84 

How to find the position of the longer axis of the solar orbit 85 — 86 

CHAPTER III. 

The causes of the change of seasons .87 — 91 

CHAPTER IV. 

Equation of time 92 

Causes which produce inequality in apparent time 93 — 95 

Equation table, <fec 96 — 98 

CHAPTER V. 

The apparent motions of the planets 99 — 102 

The sun the center of the planetary motions 103 — 104 

Copernicus — and his system 105 

CHAPTER VI. 

The Copernican system illustrated 106 — 107 

The relative distances of the planets from the sun discovered.. . .108 — 110 

The times of revolution deduced from observation Ill — 116 

Kepler's laws 117 

CHAPTER VII. 

The transits' of Venus and Mercury 118 

The sun's horizontal parallax determined 119 — 123 

CHAPTER VIII. 

The real distance to the sun determined 124 

The distance of each planet from the sun determined 125 

The magnitudes of the planets discovered 126 

CHAPTER IX. 

A general description of the solar system 127 — 132 

A table of the asteroids 133 

The velocity of light discovered 134 — 137 

General directions to acquire a correct impression of distances 

and magnitudes in the solar system 141 — 142 



CONTENTS. i x 

SECTION III. CHAPTER I. 

The moon — its periodical revolutions, &c 143 — 144 

The lunar cycle, or golden number 145 

The figure of the moon's orbit, &c% 146 

Libration of the moon 147 — 151 

CHAPTER II. 

Eclipses 152—153 

Limits of eclipses from the nodes. ■. 154 

Periodical eclipses 156 — 160 

Occultations 161 

CHAPTER III. 

The tides , 162 

The obvious connection of the tides and the moon 162 

Tides opposite to the moon explained 163 — 164 

Mass of the moon determined by the tides 165 

The great inequality of the tides explained 166 

CHAPTER IV. 

On comets, — their general description, &c 167 

Comets, planetary bodies 168 

Description of particular comets 169 — 172 

The probable effect of a comet striking the earth 173 

CHAPTER V. 

On the peculiarities of the fixed stars 174 — 175 

Their immense distance from the earth „ 176 

The new star of 1572 176 

Double and multiple stars 178 

Nebulae — and the milky -way 179 

Gradual changes of the stars in right ascension and declination, 

caused by the motion of the equator on the ecliptic 179 

Proper motion of fixed stars — how determined 180 

CHAPTER VI. 

Aberration — how discovered — and by whom 181 

Aberration illustrated 182 

Velocity of light determined by aberration 182 — 183 

Aberration — a proof of the earth's annual revolution 184 

Nutation — its cause and effects 185 

Nutation illustrated 186 

Precession of the equinoxes 188 

Precession and nutation depend on the same cause, the spheroidal 

form of the earth 189—190 



X CONTENTS. 



SEQUEL 



Problems on the terrestrial globe 191 — 196 

Problems to be solved with or without the use of of the globes. . .196 — 202 
Various problems for finding the latitude of the observer, by the 

meridian distances of the heavenly bodies 199 — 201 

Problems to be solved by the use of the celestial globe 202 — 205 

How to find the time of rising and setting of any known 

heavenly body 205—206 



ASTRONOMY. 

CHAPTER I. 
INTRODUCTION. 

Astronomy is the science which treats of the heavenly 
bodies, describes their appearances, determines their magni- 
tudes, and discovers the laws that govern their motions. 

Astronomy is divided into Descriptive, Physical, and Prac- 
tical. 

Descriptive Astronomy merely states facts and describes ap- 
pearances. 

Physical Astronomy explains the causes which bring about 
the known results. It investigates the laws which govern the 
celestial motions. 

Practical Astronomy includes observations, and all kinds of 
astronomical computations, such as the distances and magni- 
tudes of the planets, the times of their rising, setting, and 
coming in conjunction, opposition, &c. &e. 

By astronomical observations men can determine the posi- 
tion of a ship on sea, and this branch of astronomy is called 
Nautical Astronomy, and thus geography and astronomy are 
combined, and no one can fully understand geography without 
some aid from astronomy. 

Astronomy is the most ancient of all sciences, for the people 
could not avoid observing the successive returns of day and 

Define Astronomy. How is Astronomy divided ? What is Descriptive 
Astronomy ? "What is Physical ? What is Practical ? Are Geography and 
Astronomy connected ? How ? Is Astronomy a modern science ? Why 
is it allowed to be the most ancient science ? 

11 



12 ELEMENTARY ASTRONOMY. 

night, and of summer and winter. They could not fail to 
perceive that short days corresponded to winter, and long days 
to summer ; and thus the operations of agriculture, were in a 
measure connected with astronomy. 

DEFINITION OF TERMS. 

Every science has its technicalities and conventional terms ; 
and astronomy is by no means an exception to the general rule ; 
and as it will prepare the way for a clearer understanding of 
our subject, we now give a short list of some of the technical 
terms, which must be used in our composition. 

Horizon. — Every person, wherever he may be, conceives 
himself to be in the center of a circle ; and the circumference 
of that circle is where the earth and sky apparently meet. 
That circle is called the horizon; it is completely visible, how- 
ever, only on a smooth sea ; on land it is more or less broken 
and obscured by mountains and hills. 

The mathematical and astronomical horizon is a plane passing 
through the center of the earth, and a plumb line from the 
observer is perpendicular to it. 

No two places have the same horizon. 

Sphere. — A sphere, as all well know, is a perfect bail, and 
the surface of the heavens appears to all as a perfect concave 
sphere. Around every sphere in any direction is three hundred 
and sixty degrees, written thus 360°. 

Poles. — The center of any circle round a sphere, which is 
also on the sphere, is called the pole of that circle; and every 
circle round a sphere has its poles 90° distant from the circle. 

Zenith. — The zenith of any place is the point directly over 
head ; and the nadir is directly opposite to the zenith, or under 
our feet. The zenith and nadir are the poles to the horizon. 

Meridian. — When the sun (or other celestial object) in its 
diurnal course attains its highest possible elevation above the 

What is meant by the horizon? Is the horizon every \rhere visible? 
Why ? What is the true astronomical horizon ? Explain what is meant 
by a Sphere ? roles ? Degrees ? Zenith ? Meridian ? 



INTRODUCTION. 13 

horizon, it is said to be on the meridian, and the direction to 
that object just at that moment, is said to be south or north, 
according to the locality of the observer : hence, a meridian is 
an imaginary line, north and south from any point or place, 
whether it is conceived to run along the earth or through the 
heavens. If the meridian is conceived to divide both the 
earth and the heavens, it is then considered as a plane, and is 
spoken of as the plane of the meridian. 

Altitude. — The altitude of any celestial object is its perpen- 
dicular distance from the horizon, measured in degrees, there 
being 90° from the horizon to the zenith. 

The altitude and zenith distance of a body always make 90°. 

Verticals. — All lines passing from the zenith, perpendicular 
to the horizon, are called Verticals, or Vertical Circles. The 
one passing at right angles to the meridian, and striking the 
horizon at the east and west points, is called the Prime Vertical. 

Azimuth. — The angular position of a body from the meridian, 
measured on the circle of the horizon, is called its Azimuth. 

The angular position, measured from its prime vertical, is 
called its Amplitude. 

The sum of the azimuth and amplitude must always make 90 
degrees. 

When the days and nights are equal all over the earth, which 
is observed to be the fact about the 20th of March and the 23d 
of September of each year ; — then the sun in its diurnal mo- 
tion appears to describe a great circle about the earth, which 
is called the equaior. 

Then the sun (loosely speaking) appears to rise directly in 
the east and set directly in the west, as seen from all places. 

The Earth's Equator. — The Earth' s Equator is a great circle, 
east and west, and equi-distant from the poles, dividing the 
earth into two hemispheres, a northern and a southern. 

What is the altitude of any celestial object ? How is altitude measured ? 
What are vertical circles ? Through what point do all vertical circles pass ? 
What is meant by Azimuth ? What by Amplitude ? What do you under 
stand by the Earth's Equator ? 



H ELEMENTARY ASTRONOMY. 

The Celestial Equator is the plane of the earth's equator con- 
ceived to extend into the heavens. 

When the sun, or any other heavenly body, meets the celes- 
tial equator, it is said to be in the Equinox, and the equatorial 
line in the heavens is called the Equinoctial. 

Latitude. — The latitude of any place on the earth, is its dis- 
tance from the equator, measured in degrees on the meridian, 
either north or south. 

If the measure is toward the north, it is north latitude ; if 
toward the south, south latitude. 

The distance from the equator to the poles is 90 degrees — 
one-fourth of a circle ; and we shall know the circumference 
of the whole earth whenever we can find the absolute length of 
one degree on its surface. 

Co-Latitude. — Co-latitude is the distance, in degrees, of any 
place from the nearest pole. 

The latitude and co-latitude (complement of the latitude) 
must, of course, always make 90 degrees. 

Parallels of latitude are small circles on the surface of the 
earth, parallel to the equator. 

Every point, in such a circle, has the same latitude. 

Longitude. — The longitude of a place, on the surface of the 
earth, is the inclination of its meridian to some other meridian 
which may be chosen to reckon from. English astronomers 
and geographers take the meridian which runs through Green- 
wich Observatory, as the zero meridian. 

Other nations generally take the meridian of their principal 
observatories, or that of the capital of their country, as the 
first meridian ; but this is national vanity, and creates only 
trouble and confusion : it is important that the whole world 

What do you understand by the Celestial Equator ? "What is latitude 
on the earth ? How is it measured ? How many degrees are there from 
the equator to the pole ? If the earth were larger, would there be more 
degrees from the equator to the pole? What is longitude? What meri- 
dian is it reckoned from ? Why that meridian ? Could it have been from 
anv other ? 



INTRODUCTION. 15 

should agree on someone meridian, from which to reckon longi- 
tude ; but as nature has designated no particular one, it is not 
wonderful that different nations have chosen different lines. 

In this work, we shall adopt the meridian of Greenwich as 
the zero line of longitude, because most of the globes and 
maps, and all the important astronomical tables, are adapted to 
that meridian, and we see nothing to be gained by changing it. 

Declination. — Declination refers only to the celestial equator, 
and is a leaning or declining, north or south of that line, and it 
is similar to latitude on the earth. 

Solsticial points. — The points, in the heavens, north and 
south, where the sun has its greatest declination, are the solsti- 
cial points. 

The northern point we call the Summer Solstice, and the 
southern point the Winter Solstice; the first is in longitude 90°, 
the second in longitude 270°. 

As latitude is reckoned north and south, so longitude is 
reckoned east and west ; but it would add greatly to syste- 
matic regularity, and tend much to avoid confusion and am- 
biguity in computations, were this mode of expression aban- 
doned, and longitude invariably reckoned westward, from to 
360 degrees. 

Declination in the heavens is similar to latitude on the earth. 
If a person were in 20° north latitude when the sun's declina- 
tion was 20° north, the sun at noon would then be in his zenith, 
or pass directly over his head. 

Ecliptic. — The ecliptic is a great circle in the heavens, along 
which the sun appears to pass in a year, extending from about 
23£ degrees of south declination to about 23|- degrees of north 
declination in the opposite longitude of the heavens. This 
circle is called the ecliptic, because all eclipses, both of the 
sun and moon, take place when the moon is either in or near it. 

What is decimation ? What is the declination of the north pole ? What 
are the solsticial points ? In what latitude are they ? What circle is the 
sun always in ? Why is that circle called the ecliptic ? 



1 6 ELEMENTARY ASTRONOMY. 

Equator and Ecliptic. — The celestial equator and the ecliptic 
are two great circles, in the heavens, which intersect each 
other (at the present day) by an angle of about 23° 27' 32". 

The sun, in its apparent annual motion, runs round the heav- 
ens, crosses the equator from the south to the north on the 
20th of March of each year, and re-crosses from the north to 
the south on the 23d of September. 

The point on the ecliptic where the sun mee.ts the celestial 
equator in the spring, is taken as the zero point from which to 
reckon longitude, in astronomy, eastward along the ecliptic. 
This point is called the Vernal Equinox. 

From the same point eastward along the equator is reckoned 
right ascension, and it is counted from degrees to 360 degrees, 
or from hours to 24 hours ; 15 degrees of arc corresponding 
to one hour in time. 

Zodiac. — Ancient astronomers defined the zodiac to be a 
space in the heavens sixteen degrees wide, eight degrees on 
each side of the ecliptic, and quite round the sphere : the 
ecliptic was therefore the center of the zodiac. The ecliptic, 
or zodiac, was divided into twelve signs, called signs of the 
zodiac, each sign was therefore 30° in extent. 

The first sign, commencing at the vernal equinox, is called 
Aries, and the character denoting it is written thus r jf'. 

The sun enters the 12 signs as follows : 

Aries (°f) on the 20th of March ; Taurus (\j) on the 19th 
of April ; Gemini ( J[) on the 20th of May ; Cancer (6§) on 
the 21st of June ; Leo (<Q) on the 22d of July ; and Virgo{W) 
on the 22d of August. 

The foregoing are called northern signs, because the sun 
must have north declination while the sun is in them. 

The following are designated as the southern signs of the 

Does the ecliptic intersect the equator? At what angle ? "What point 
in the heavens is called the Vernal Equinox ? What is the Zodiac ? What 
ia meant by the signs of the Zodiac ? When does the sun enter the first 
sign of the Zodiac ? 



INTRODUCTION. 17 

zodiac, because the sun must have south declination while he 
is in them : 

The sun enters Libra (lqj) on the 23d of September; Scorpio 
(T)1 ) on the 22d of October ; Sagittarius (^[) on the 22d of 
November ; Capvicomus (/5) on ^ ne ^lst °f December ; Aqua- 
rius (*») on the 20th of January ; and Pisces ()-() on the 19th 
of February. Passing through this last sign the sun again 
enters (^p) on the 20th of March, to perform the revolution 
over again, and thus it goes on year by year. 

The zodiac and signs of the zodiac being but the offspring 
of astrology and heathen mythology, they are entirely dis- 
carded by modern astronomers ; yet they still linger in country 
almanacs and in many school books, and it is with reluctance 
that we even mention them. They are of no use, even as 
points of reference, and they embrace no scientific principle 
whatever. 

Conjunction. — When two celestial bodies have the same lon- 
gitude, they are said to be in conjunction. 

When two celestial bodies have the same right ascension, that 
is, come to the meridian at the same time, they are said to be in 
conjunction in right ascension. 

Opposition. — When two celestial bodies have a difference of 
longitude of 1 80 degrees, they are said to be in opposition. 

Direct. — Direct, in astronomy, is a motion to the eastward 
among the stars. 

Retrograde. — Retrograde is a motion to the westward among 
the stars. Stationary means apparently so in respect to the 
stars. Other terms not here mentioned will be explained as 
we use them. 

Why are some of the signs called northern, and others southern signs ? 
Is the distinction of signs necessary ? What is meant by conjunction ? 
By opposition ? What by direct ? Retrograde ? 

2 



18 ELEMENTARY ASTRONOMY. 

CHAPTER II. 
PRELIMINARY OBSERVATIONS. 

To commence the study of astronomy, we must observe and 
call to mind the real appearance of the heavens. 

Take such a station, any clear night, as will command an 
extensive view of that apparent, concave hemisphere above us, 
which we call the sky, and fix well in the mind the directions 
of north, south, east, and west. 

At first, let us suppose the observer to be somewhere in the 
United States, or somewhere in the northern hemisphere, about 
40 degrees from the equator. 

Soon he will perceive a variation in the position of the 
stars : those at the east of him will apparent!} 7 rise ; those at 
the west will appear to sink lower, or fall below the horizon ; 
those at the south, and near his zenith, will apparently move 
westward ; and those at the north of him, which he may see 
about half way between the horizon and the zenith, will appear 
stationary. 

Let such observations be continued during all the hours of 
the night, and for several nights, and the observer cannot fail 
to be convinced that not only all the stars, but the sun, moon, 
and planets, appear to perform revolutions, in about twenty- 
four hours, round a fixed point ; and that fixed point, as ap- 
pears to us (in the middle and northern part of the United 
States), is about midway between the northern horizon and 
the zenith. 

It should always be borne in mind that these motions are 

How can a person convince himself that seme of the stars have an appa- 
rent motion from east to west, like the sun in the day time ? Do all the 
stars have such an apparent motion, as seen from this place ? "What stars 
do not? 



PRELIMINARY OBSERVATIONS. 19 

but apparent, the stars keeping the same positions with respect 
to each other, whether they are rising or falling, or north or 
south of the observer, and the general aspect of the heavens is 
the same now, as it was in the very earliest ages of astronomy, 
and will be the same in ages to come. 

All the heavenly bodies, whether sun, moon, planets, or 
stars, appear to have a diurnal motion round a fixed 'point, and 
all those stars which are 90 degrees from that point, appa- 
rently describe a great circle. Those stars which are nearer 
to the fixed point than 90 degrees, describe smaller circles; and 
the circles are smaller and smaller as the objects are nearer 
and nearer the fixed point. 

There is one star so near this fixed point, that the small cir- 
cle it describes, in about 24 hours, is not apparent from mere 
inspection. To detect the apparent motion of this star, we 
must resort to nice observations, aided by mathematical in- 
struments. 

This fixed point, that we have several times mentioned, is the 
Worth Pole of the heavens, and this one star that we have just 
mentioned, is commonly called the North Star, or the Pole 
Star. 

As the North Star appears stationary, to the common ob- 
server, it has always been taken as the infallible guide to 
direction; and every sailor of the ocean, and every wanderer 
of the African and Arabian deserts, has held familiar acquain- 
tance with it. 

If our observer now goes more to the southward, and makes 
the same observations on the apparent motions of the stars, he 
will find the same general results ; each individual star will 
describe the same circle ; but the pole, the fixed point, will be 
lower down, and nearer to the northern horizon ; and it will be 

Those stars that do not rise and set, what motion, real or apparent, do 
they have ? Is any star apparently stationory ? Is there a star just at the 
north pole ? What use has been made of the north star ? If a person 
should go south from this place, "what apparent effect "would that have on 
the north star, as viewed by him ? 



20 ELEMENTARY ASTRONOMY. 

lower and lower in proportion to the distance the observer goes 
to the south. After the observer has gone sufficiently far, the 
fixed point, the pole, will no longer be up in the heavens, but 
down in the northern horizon ; and when the pole does appear 
in the horizon, the observer is at the equator, and from that 
line all the stars at or near the equator appear to rise up di- 
rectly from the east, and go down directly to the west ; and all 
other stars, situated out of the equator, describe their small 
circles parallel to this perpendicular equatorial circle. 

If the observer goes south of the equator, the north pole will 
sink below his horizon, and the south polar point will appear 
to rise up above his horizon, and it will rise more and more as 
he goes farther and farther south ; and if he could possibly get 
to the south pole on the earth, the south pole of the apparent 
revolving heavens would be right over his head, and the equa- 
tor of the heavens would bound his horizon. 

In a similar manner if an observer goes north, the north pole 
to him would appear to rise in the heavens; and should he con- 
tinue to go north, he would finally find the pole in his zenith, 
and all the stars would apparently make circles round the 
zenith, as a center, and parallel to the horizon; and the horizon 
itself would be the celestial equator. 

When the north pole of the heavens appears at the zenith, 
the observer must then be at the north pole, on the earth, or 
at the latitude of 90 degrees. 

Any celestial body, which is north of the equator, is always 
visible from the north pole of the earth ; hence, the sun, which 
is north of the equator from the 20th of March to the 23d of 
September, must be constantly visible during that period, in a 
clear sky. 

Just as the sun comes north of the equator, its diurnal pro- 
gress, or rather, the progress of 24 hours, is around the horizon. 
When the sun's declination is 10 degrees north of the equator, 

What is the apparent diurnal motion of the stars, as seen from the equa- 
tor ? "What from the south pole ? What part of the heavens bounds the 
horizon as seen from the south pole ? What from the north pole ? 



PRELIMINARY OBSERVATIONS. 21 

the progress of the sun, in 24 hours, as seen from the north pole, 
is around the horizon at an altitude of about 10 degrees ; and 
so on for any other degree. 

From the north pole, all directions on the surface of the earth 
are south. North, strictly speaking, would be in a vertical 
direction, which would make the absolute south directly down 
towards the center of the earth. 

We have observed that the pole of the heavens rises as we 
go north, and sinks toward the horizon as we go south ; and 
when we observe that the pole has changed its position ona 
degree, in relation to the horizon, we know that we must 
have changed place one degree on the surface of the earth. 

Now we know by observation, that if we go north about 69£ 
English miles on the earth, the north pole will be one degres 
higher above the horizon. Therefore 69^ miles corresponds t > 
one degree, on the earth ; and hence, the whole circumference 
of the earth must be 69^ multiplied by 360 : for there are 360 
degrees to every circle. This gives 24,930 miles for the cir- 
cumference of the earth, and 7,930 miles for its diameter, which 
is not far from the truth. 

Here, in the United States, or anywhere either in Europe, 
Asia, or America, north of the equator, say in latitude 40 de- 
grees, the north pole of the heavens must appear at an altitude 
of 40 degrees above the horizon ; and as all the stars and 
heavenly bodies apparently circulate round this point as a center, 
it follows that all those stars which are within 40 degrees of the 
pole, can never go below the horizon, but circulate round and 
round the pole. All those stars which never go below the 
horizon, are called circumsolar stars, 

At the north, and very near the north pole, the sun is a cir- 
compolar body while it is north of the equator, and it is a 

Describe the apparent diurnal motion of the sun from the north pole 
when its declination is 15 degrees north ? How far must we go north or 
south on the earth to change the apparent altitude of the pole one degree ? 
What does that show ? What is meant by circumpolar stars ? Would the 
term circumpolar apply if the observer were at the equator ? 



22 ELEMENTARY ASTRONOMY. 

cireumpolar body as seen from the south pole, while it is south 
of the equator ; this gives six months day and six months 
night, at the poles. 

North of latitude 66 degrees, and when the sun's declina- 
tion is more than 23 degrees north (as it is on and about the 
20th of June in each year), then the sun comes at, or very 
near, the northern horizon, at midnight ; it is nearly east, at 6 
o'clock in the morning; it is south, at noon, and about 23 de- 
grees in altitude ; and is nearly west at 6 in the afternoon. 

In all latitudes and from all places on the earth, the sun ia 
observed to circulate round the nearest pole, as a center ; and 
when the sun is on the same side of the equator as the obser- 
ver, more than half of the sun's diurnal circle is above the ho- 
rizon, and the observer will have more than 12 hours sunlight. 

When the sun is on the equator, the horizon, of every lati- 
tude, cuts the sun's diurnal circle into two equal parts, and 
gives 12 hours day and 12 hours night, the world over. 
When the sun is on the opposite side of the equator from the 
observer, the smaller segment of the sun's diurnal circle is 
above the horizon, and, of course, gives shorter days than 
nights. 

We have, thus far, made but rude and very imperfect ob- 
servations on the apparent motion of the heavenly bodies, and 
have satisfied ourselves only of two facts : 

1st. That all the stars, sun, moon, and planets, included, 
apparently circulate round the pole, and round the earth, in a 
day, or in about 24 hours. 

2d. That the sun comes to the meridian, at different alti- 
tudes above the horizon, at different seasons of the year, giv- 
ing long days in June, and short days in December, in all 
northern latitudes. 

Describe the appearance of the sun, during 24 hours, as seen from 
latitude Q6 degrees north, when the sun's declination is 23 degrees north. 
Describe the diurnal appearance of the sun, as seen from the north pole, 
when the sun is on the equator, when its declination is IS decrees north. 
What two facts are thus far established ? 



PRELIMINARY OBSERVATIONS. 23 

Let us now pay attention to some other particulars. Let us 
look at the different groups of stars, and individual stars, so 
that we can recognize them night after night. 

By a little systematic observation, which we shall describe 
a little further on, or even without any particular system of 
observation, almost any one is able to recognize certain stars, 
or groups of stars, such as the Seven Stars, the Belt of Orion, 
Aldebaran, Sirius, and the like, and having likewise the use of 
a clock, he can observe when any particular star comes to any 
definite position. 

Let a person place himself at any particular point, to the 
north of any perpendicular line, as the edge of a wall or build- 
ing, and let him observe the stars as they pass behind the 
building, in their diurnal motions from the east to the west. 
For example, let us suppose that the observer is watching the 
star Aldebaran, and that, when the eye is placed in a particu- 
lar definite position, the star passes behind the building at 
exactly 8 o'clock. 

The next evening, the same star will come to the same point 
about 4 minutes before 8 o'clock ; and it will not come to the 
same point again, at 8 o'clock in the evening, until after the 
expiration of one year. 

But in any year, on the same day of the month, and at the 
same hour of the day, the same star will be at, or very near, 
the same position, as seen from the same point. 

For instance, if certain stars come on the meridian at a par- 
ticular time in the evening, on the first day of December, the 
same stars will not come on the meridian again, at the same 
time of the night, until the first day of the next December. 

On the first of January, certain stars come to the meridian 
at midnight ; and (speaking loosely) every first of January the 
same stars come to the meridian at the same time ; and there 

Does the same fixed star come to the meridian at the same hour every 
night ? Does it come to the meridian earlier or later ? If a star come to 
the meridian at 10 o'clock in the evening any particular night, when will 
it come to the meridian as^ain at the same time in the evening- ? 



24 ELEMENTARY ASTRONOMY. 

will be no other day during the whole year, when the same 
stars will come to the meridian at midnight. 

Thus, the same day of every year is observed to have the 
same position of the stars at the same hour of the night ; and 
this is the most definite index for the exjiiration of a year. 

The year is also indicated by the change of the sun's decli- 
nation, which the most careless observer cannot fail to notice. 
On the 21st of June, the sun declines about 23^- degrees from 
the equator towards the north ; and, of course, to us in the 
northern hemisphere, its meridian aliitude is so much greater, 
and the horizontal shadows it casts from the same fixed objects 
will be shorter ; and the same meridian altitude and short 
shadow will not occur again until the following JLune, or after 
the expiration of one year. 

Thus, we see, that the time of the stars cominp; on to the 
meridian, and the declination of the sun, have a close corres- 
pondence, in relation to time. 

In all our observations on the stars, we notice that their 
apparent relative situations are not changed by their diurnal 
motions. In whatever parts of their circles they are observed, 
or at whatever hour of the night they are seen, the same con- 
figuration is recognized, although the same group, in the dif- 
ferent parts of its course, will stand differently, in respect to 
the horizon. For instance, a conficmration of stars resembling 
the letter A, when east of the meridian, will resemble the let- 
ter V, when west of the meridian. 

As the stars, in general, do not change their positions in 
respect to each other, they are called fixed stars ; but there are 
a few important stars that do change, in respect to other stars ; 
and for that reason they become especial objects of attention, 
and form the most interesting portion of astronomy. 

In the earliest ages, those stars that changed their places, 

What is the most definite index of the expiration of a year ? What 
other index is there of the expiration of a year ? Do the stars change their 
configuration really or apparently while performing their diurnal circles? 
Explain. 



PRELIMINARY OBSERVATIONS. 25 

were called wandering stars; and they were subsequently found 
to be the planetary bodies of the solar system, like the earth 
on which we live ; or rather, the earth on which we live, after 
strict investigation, was found to be a planet belonging to that 
class of wandering stars ; and this striking fact gives to astron- 
omy much of its sublimity and importance. In a subsequent 
part of this work we hope to be able to explain to the general 
reader how science developed this and other facts, but at pre' 
sent they must all be taken on authority. 

The fixed stars come to the meridian at intervals of 23h. 3m. 
56.555s. of mean solar time, and if any star should be observed 
coming to the meridian at a greater interval of time, then that 
star could not be a fixed star, but a planet, or comet, whose 
motion was then eastward. But if the interval be less than 
23h. 3m. 56s., the star is then wandering towards the west, and 
is said to be retrograding. 

The planets of our system, sometimes wander eastward — 
sometimes westward — and sometimes they appear stationary ; 
but the eastward motion prevails, and all the planets appear to 
make revolutions round the earth from west to east. 

The apparent irregularities of their motions, are perfectly 
natural results, arising from the motion of the earth round the 
sun; and these facts are brought in to show that the earth does 
revolve round the sun, and is, in fact, a planet. 

To study astronomy properly, it is not sufficient to read it 
off the pages of a book ; we must read it off of the face of the 
sky ; and before we can do that, we must be better acquainted 
with the face of the sky than we are at present, and that will 
be the object of the following chapter. 

What stars became objects of special attention to the ancients ? Is tLe 
earth one of a class of stars ? Was this known in an early day ? 



26 ELEMENTARY ASTRONOMY. 

CHAPTER III. 

THE FIXED STARS — AS CELESTIAL LOCALITIES. 

The fixed stars are the only landmarks in astronomy, in 
respect to both time and space. They seem to have been 
thrown about in irregular and ill-defined groups and clusters, 
called constellations. The individuals of these groups and 
clusters differ greatly as to brightness, hue, and color ; but 
they all agree in one attribute — a high degree of permanence, 
as to their relative positions in the group ; and the groups are 
as permanent in respect to each other. This has procured 
them the title of fixed stars; an expression which must be 
understood in a comparative, and not in an absolute, sense ; 
for, after long investigation, it is ascertained that some of 
them, if not all, are in motion ; although too slow to be percep- 
tible, except by very delicate observations, continued through 
a long series of years. 

The stars are also divided into different classes, according to 
their degree of brilliancy, called magnitudes. There are six 
magnitudes, visible to the naked eye ; and ten telescopic mag- 
nitudes — in all, sixteen. 

The brightest are said to be of the first magnitude ; those less 
bright, of the second magnitude, etc.; the sixth magnitude is 
just visible to the naked eye. 

The stars are very unequally distributed among these classes; 
nor do all astronomers agree as to the number belonging to 
each ; for it is impossible to tell where one class ends and 
another begins ; nor is it important, for all this is but a matter 
of fancy, involving no principle. In the first magnitude there 

What are constellations ? In what sense should we apply the term fixed 
stars ? What is meant by the magnitude of a star ? How many classes 
of magnitudes are there ? Can we define where one class of magnitudes 
begins or ends ? 



THE FIXED STARS. 27 

is really but one star (Sirius) ; for this is manifestly brighter 
than any other ; but most astronomers put fifteen or twenty 
into this class. 

The second magnitude includes from fifty to sixty ; the third 
about two hundred, the numbers increasing very rapidly, as 
we descend in the scale of brightness. 

From some experiments on the intensity of light, it has been 
determined, that if we put the light of a star, of the average 
1st magnitude, 100, we shall have : 

1st magnitude =100 4th magnitude = 6 

2d " = 25 5th " =2 

3d " = 12 6th " = 1 

On this scale, Sir William Herschel placed the brightness of 

Sirius at 320. 

Ancient astronomy has come down to us much tarnished 
with superstition and heathen mythology. Every constellation 
bears the name of some pagan deity, and is associated with 
some absurd and ridiculous fable; yet, strange as it may 
appear, these masses of rubbish and ignorance — these clouds 
and fogs, intercepting the true light of knowledge, are still not 
only retained, but cherished, in many modern works, and dig- 
nified with the name of astronomy.* 

* As a specimen of what "was once called astronomy, and is even no"v» 
studied for astronomy in some female boarding schools, we give the follow- 
ing extracts, taken from Keith on the globes. To say nothing of other 
branches of knowledge, we congratulate the learner that ancient fables no 
longer obscure astronomy. 

" Coma Berenices is composed of the unformed stars, between the Lion'fc 
tail and Bootes. Berenice was the wife of Evergetes, a surname signifying 
benefactor : when he went on a dangerous expedition, she vowed to dedi- 
cate her hair to the goddess Venus, if he returned in safety. Sometime 
after the victorious return of Evergetes, the locks which were in the temple 
of Venus, disappeared ; and Conon, an astronomer, publicly reported that 
Jupiter had carried them away, and made them a constellation. 

" Cor Caroli, or Charles's heart, in the neck of Chara, the southernmost 
of the two dogs held in a string by Bootes, was so denominated by Sir 
Charles Scarborough, physician to king Charles II, in honor of King 
Charles I." 

How many stars are there in the first magnitude ? What is said of an- 
cient superstition, and mythology? 



28 ELEMENTARY ASTRONOMY. 

Merely as names, either to constellations or to individual 
stars, we shall make no objections ; and it would be useless, if 
we did; for names long known, will be retained, however im- 
proper or objectionable ; hence, when we speak of Orion, the 
Little Bog, or the Great Bear, it must not be understood that 
we have any great respect for mythology. 

It is not our object now to give any very minute or scien- 
tific description of the starry heavens — such as pointing out 
the variable, double, and multiple stars — the Milky Way, and 
nebulce; these will receive special attention in some future 
chapter : at present, our only aim is to point out the method of 
obtaining a knowledge of the mere appearance of the sky, to 
the common observer, which may be called the geography of 
the heavens. 

To give a person an idea of locality, on the earth, we refer 
to points and places supposed to be known. Thus, when we 
say that a certain town is 15 miles northwest of Boston, or 
that a ship is 100 miles east of the Cape of Good Hope, or 
that a certain mountain is 10 miles north of Calcutta, we have 
a pretty definite idea of the locality of the town, the ship, and 
the mountain, on the face of the earth., provided we have a 
clear idea of the face of the earth, and know the position of 
Boston, the Cape of Good Hope, and Calcutta. 

So it is with the geography of the heavens ; the apparent 
surface of the whole heavens must be in the mind, and then 
the localities of certain bright stars must be known, as land- 
marks, like Boston, the Cape of Good Hope, and Calcutta. 

"We shall now make some effort to point out these landmarks. 
The Xorth Star is the first, and most important to be recog- 
nized ; and it can always be known to an observer, in any 
northern latitude, from its stationary appearance and altitude ; 
which is never more than one and a half degrees from the lati- 
tude of the observer. Thus, a person in 10° north latitude, 

How does the author regard mythology? What is meant by the 
geography of the heavens? What star is the most important to be recog- 
nized ? How can it be known ? 



THE FIXED STARS. 



29 



will find the north star very nearly in a northern direction, 
between 8° and 12° above the northern horizon. An observer 
in 25° north latitude, will find the north star nearly north in 
direction, and between 24° and 26° of altitude, and so on for 
any other northern latitude. It is by such observations on the 
north star, that latitude can be found. 

When the influence of refraction is allowed for, the latitude of a 
place is midway between the greatest and least altitudes of the north 
star. 




We have here attempted to make a faint representation of the 
region about the north pole to the distance of 40°. The hours 
are hours of right ascension in the heavens. The pole star is 
nearly (not exactly) in the center of this circle. Directly 

What star is always very nearly north ? What is the latitude of any 
place in the northern hemisphere equal to ? 



30 ELEMENTARY ASTRONOMY. 

opposite the cup or Great Bear, is the constellation Cassiopea. 
JE is the position of the pole of the ecliptic, and a little south 
of E, in right ascension, about 18 hours, is the constellation 
called the Dragon or Draco. At the distance of about 32 de- 
grees from the pole, are seven bright stars, between the 1st 
and 2d magnitudes, forming a figure resembling a dipper, four 
of them forming the cup, and three the handle. They occupy 
a space between the right ascension of lOh. 45m. and 13h. 40m. 
The two stars forming the sides of the cup, opposite to the han- 
dle, are always in a line with the North Star, and are therefore 
called pointers : they always point to the North Star. The line 
joining the equinoxes, or the first meridian of right ascension, 
runs from the pole, between the other two stars forming the 
cup. The first star in the handle, nearest the cup, is called 
Alioth, the next Mizar, near which is a small star, of the 4th 
magnitude ; the last one is Benetnasch. The stars in the han- 
dle are said to be in the tail of the Great Bear. 

About four degrees from the pole star, is a star of the 3d 
magnitude, e Ursce Minoris. A line drawn through the pole 
(not pole star) and this star, will pass through, or very near, 
the poles of the ecliptic and the tropics. A small constellation, 
near the pole, is called Ursa Minor, or the Little Bear. An 
irregular semicircle of bright stars, between the dipper and 
the pole, is called the Serpent. 

If a line be drawn from e Ursce Minoris, through the pole 
star, and continued about 45 degrees, it will strike a very beau- 
tiful star, of the 1st magnitude, called Capella. Within five 
degrees of Capella are three stars, of about the 4th magnitude, 
forming a very exact isosceles triangle, the vertical angle about 
28 degrees. A line drawn from Alioth, through the pole star, 
and continued about the same distance on the other side, passes 
through a cluster of stars called Cassiopea in her chair. The 

"Why are two certain stars called pointers ? Wl at small constellation 
is near the north pole ? What stars are in the handle of the cup, or in the 
tail of the Great Bear ? 



THE FIXED STARS. 31 

principal star in Cassiopea, with the pole star and Capella, form 
an isosceles triangle, Capella at the vertex. 

More attention has been paid to the constellations along the 
equator and ecliptic, than to others in remoter regions of the 
heavens, because the sun, moon, and planets, apparently traverse 
through them. 

There are nine bright stars near the ecliptic, which are used 
by seamen, in connection with the position of the moon, to find 
longitude from, — and for this reason these stars are called lunar 
stars. Their proper names are Arietls, Aldebaran, Pollux, Peg- 
ulus, Spica, Antares, Aquilce, Fomalhaut, and Pegasi. 

Beginning with the first point of Aries as it now stands, no 
prominent stars are near it ; and, going along the ecliptic to the 
eastward, there is nothing to arrest special attention, until we 
come to the Pleiades, or Seven Stars, though only six are visible 
to the naked eye. This little cluster is so well known, and so 
remarkable, that it needs no description. Southeast of the. 
Seven Stars, at the distance of about 1 8 degrees, is a remark- 
able cluster of stars, said to be in the Bull's Bead; the largest 
star in this cluster is of the 1st magnitude, of a red color, 
called Aldebaran. It is one of the nine stars selected as points 
from which to compute the moon's distance, for the assistance 
of navigators. 

This cluster resembles an A when east of the meridian, and 
a V when west of it. The Seven Stars, Aldebaran, and Capella, 
form a triangle very nearly isosceles — Capella at the vertex. 
A line drawn from the Seven Stars, a little to the west of Alde- 
baran, will strike the most remarkable constellation in the 
heavens, Orion, (it is out of the zodiac however) ; some call it 
the Ell and Yard. The figure is mainly distinguished by three 
stars in one direction, within two degrees of each other ; and 
two other stars, forming, with one of the three first mentioned, 
another line at right angles with the first line. 

Why are certain stars called lunar stars ? Is there any star near the first 
point of Aries ? What is meant by the first point of Aries ? What bright 
star is about 18° southeast of the Seven Stars ? How would you find Orion 
on seeing the Seven Stars and Aldebaran ? 



32 ELEMENTARY ASTRONOMY. 

The five stars thus in lines, are of the 1st or 2d magnitude. 
A line from the Seven Stars, passing near Aldebar an and through 
Orion, will pass very near to Sirius, the most brilliant star in 
the heavens. The ecliptic passes about midway between the 
Seven Stars and Aldebaran, in nearly an eastern direction. 
Kearly due east from the northernmost and brightest star in 
Orion, and at the distance of about 25 degrees, is the star 
Procyon ; a bright, lone star. 

The northernmost star in Orion, with Sirius and Procyon, 
form an equilateral triangle. 

Directly north of Procyon, at the distances of 25 or 30 
degrees, are two bright stars, Castor and Pollux. Castor is 
the most northern. Pollux is one of the nine lunar stars. 
Thus we might run over that portion of the heavens which is 
ever visible to us, and by this method every student of astro- 
nomy can render himself familiar with the aspect of the sky ; 
but it is not sufficiently definite and scientific to satisfy a ma- 
thematical mind. 

The only scientific method of defining the position of a place 
on the earth, is to mention its latitude and longitude; and this 
method fully defines any and every place, however unimpor- 
tant and unfrequented it may be : so in astronomy, the only 
scientific method of defining the position of a star, is to men- 
tion its latitude and longitude, or, more conveniently, its right 
ascension and declination. 

It is not sufficient to tell the navigator that a coast makes 
off in such a direction from a certain point, and that it is so 
far to a certain cape ; and, from one cape to another, it is about 
40 miles south-west — he would place very little reliance on 
any such directions. To secure his respect, and command his 
confidence, the latitude and longitude of every point, promon- 
tory, river, and harbor, along the coast, must be given ; and 
then he can shape his course to any point, or strike in upon it 

What three bright stars form an equilateral triangle ? Where is Castor 
and Pollux? What is the scientific method of defining a place on the 
earth ? What of locating a star in the heavens ? 



THE FIXED STARS. 33 

from the indefinite expanse of a pathless sea. So with an 
astronomer ; while he understands and appreciates the rough 
and general descriptions, such as we have just given, he re- 
quires the certain description, comprised in right ascension and 
declination.. 

Accordingly, astronomers have given the right ascensions 
and declinations of every visible star in the heavens (and of 
very many that are invisible), and arranged them in tables, 
in the onW of right ascension. 

There are far too many stars, for each to have a proper 
name ; and , for the sake of reference, Mr. John Bayer, of 
Augsburg, in Suabia, about the year 1603. proposed to denote 
the stars by the letters of the Greek and Roman alphabets ; 
by placing the first Greek letter a to the principal star in the 
constellation, /? to the second in magnitude, y to the third, and 
so on ; and if the Greek alphabet shall become exhausted, then 
begin with the Roman, a, b, c, etc. 

" Catalogues of particular stars, in sections of the heavens, 
have been published by different astronomers, each author 
numbering the individual stars embraced in his list, according 
to the places they respectively occupy in the catalogue." 
These references to particular catalogues are sometimes marked 
on celestial globes, thus : 79 H, meaning that the star is the 
79th in Herschel's catalogue ; 37 M, signifies the 37th num- 
ber in the catalogue of Mayer, etc. 

Among our tables will be found a catalogue of a hundred of 
the principal stars, inserted for the purpose of teaching a definite 
and scientific method of making a learner acquainted with the 
geography of the heavens, which will be given in another chapter. 

What did John Bayer propose ? How are stars, in sectional catalogues, 
referred to ? 



34 ELEMENTARY ASTRONOMY. 

CHAPTER IV. 

TIME — AND THE MEASURE OF TIME. 

Time is but a measured portion of unlimited duration — and 
it is measured off, directly or indirectly, by astronomical events. 

The most obvious astronomical event is that of a natural day, 
from sunrise to sunset, or from sunrise to sunrise again, — but 
as these intervals are variable in length, they are not proper 
standards for time. 

The interval embracing the four seasons of the year, i3 
another astronomical period which serves to measure time on 
a large and indefinite scale. 

The interval from full moon to full moon again, is also an 
astronomical period, — but after careful observation, it has 
been found to be a period of variable duration ; and, moreover, 
it is impossible for the unlearned to define the moment when 
such an interval begins or ends, — therefore this period is use- 
less, as a measure of time — and none but savages pretend to 
use it as such. 

For a standard of measure, we must find, if possible, some 
invariable period that can be distinctly defined. In the early 
ages of astronomy, the interval from noon, to noon again, was 
considered a constant interval, and taken for the measure of 
time, — and for the common business of the world, this will 
be the standard for time, because it is the most obvious, natu- 
ral, and convenient. But after close investigation and careful 
observations, this interval was found to be slightly variable, 
and another interval, the passage of a fixed star from the meri- 
dian to the meridian again, was found to be a constant interval, 
therefore this interval is taken as the standard measure of time. 

What is time ? What is an astronomical event ? Is from noon to noon, 
by the sun, an invariable interval of time ? What astronomical events 
mark equal intervals of time ? • 



TIME— AND THE MEASURE OF TIME. 35 

The interval from one passage of a star across the meridian, 
to the next, is a sidereal day, and measured by the common 
solar clock, the interval is 23h. 56m. 4.09s. No matter what 
star is observed, the interval is the same, and as this has been 
the universal experience of astronomers in all ages, it com- 
pletely establishes the fact, that all the fixed stars come to the 
meridian in exactly equal intervals of time ; and this gives us 
a standard measure for time, and the only standard measure, 
for all other motions are variable and unequal. 

Again, this interval must be the time that the earth employs 
in turning on its axis ; for if the star is fixed, it is a mark for 
the time, that the meridian is in exactly the same position in 
relation to absolute space. 

Soon after the fact was established that the fixed stars came 
to the meridian in equal times, and that interval less than 24 
hours, astronomers conceived the idea of graduating a clock to 
that interval, and dividing it into 24 hours. Thus graduating 
a clock to the stars, apd not to the sun, it is therefore called a 
sidereal, and not a solar, or common clock ; and as it was sug- 
gested by astronomers, and used only for the purposes of 
astronomy, it is also very appropriately called an astronomical 
clock; but save its graduation, and the nicety of its construc- 
tion, it does not differ from a common clock. 

With a perfect astronomical clock, the same star will pass the 
meridian at exactly the same time, from one year's end to another. 
If the time is not the same, the clock does not run to sidereal 
time ; and the variation of time, or the difference between 
the time when the star passes the meridian, and the time 
which ought to be shown by the clock, will determine the rate 
of the clock. And with the rate of the clock, and its error, we 
can readily deduce the true time from the time shown by the 
face of the clock. We have several times mentioned the fact, 
that the same star returns to the same meridian again and 

What is a sidereal day ? What is an astronomical clock ? How does 
it differ from a common clock ? How can we determine whether the as- 
tronomical clock moves perfectly or not ? 



36 ELEMENTARY ASTRONOMY. 

again, after every interval of 24 sidereal hours. So, two differ- 
ent stars come to the meridian at constant and invariable 
intervals of time from each other ; and by such intervals we 
decide how far, or how many degrees, one star is east or west 
of another. For instance, if a certain fixed star was observed 
to pass the meridian when the sidereal clock marked 8 hours, 
and another star was observed to pass at 9, just one sidereal 
hour after, then we know that the latter star is on a celestial 
meridian, just 15 degrees eastward of the meridian of the firs* 
mentioned star. 

With a perfect astronomical clock, or one which shows true 
sidereal time, we can find the right ascension of any heavenly 
body, by simply observing the time it passes the meridian. 
For right ascension is but another term for the sidereal time the 
body passes the meridian. 

That meridian in the heavens which passes through the point 
where the ecliptic and equator intersect, at the first point of 
Aries, the point where the sun crosses the equator in the spring, 
is taken as the first meridian of right ascension, and from thence 
we reckon eastward, from hours to 24 hours, to the same 
meridian again. 

This being the case, the sidereal clock should show Oh. Om. 
Os. when the equinox is on the meridian ; and, if a star or a 
planet were observed to pass the meridian at 4h. 20m, 30s., 
then the right ascension of that star or planet, at that time, 
was 4h. 20m. 30s. 

This, however, is on the supposition that the clock is perfect, 
and runs perfectly uniform, which is never the case ; unfor- 
tunately, there is no such thing as a perfect clock, and the 
difficulties thus arising, must be surmounted by artifice and 
multiplied observations. 

Just as the sun crosses the equator in the spring, its right 

How can we find the rate of the clock ? What difference is there be- 
tween true sidereal time and right ascension ? Define the first astronom- 
ical meridian ? What time should the clock show when the equinox is on 
the meridian? 



TIME— AND THE MEASURE OF TIME. 37 

ascension is Oh., and from this, its right ascension increases 
abont four minutes each day ; this shows that the sun has an 
apparent motion eastward, among the stars. 

The right ascensions of all the fixed stars increase at a very- 
slow rate, in consequence of the precession of the equinoxes, that 
is, a slow motion of the first meridian to the westward, among 
the stars, of about 50"1 per year ; this gives the stars the appear- 
ance of moving eastward and increasing their right ascensions. 
The entire increase since the first reliable observations on 
record, is about 30°, or 2 hours. 

The great multitude of stars retain the same relative right 
ascensions, and the same relative declinations, for very long 
periods of time, — that is, they retain the same positions with 
respect to each other. But occasionally, stars may be observed 
that change their right ascension from day to day, and these 
stars, in early times, were called wandering stars — mentioned 
in the preceding chapter, — they are the planets of our system, 
the earth itself being one of them. 

When it is discovered that a star does not pass the meridian 
at equal intervals of time, as shown by a good astronomical 
clock, we then decide that that star must have a motion of its 
own — and of course must be a planet or a comet. 

The reason why astronomers commence the day at noon 
rather than at midnight, is because noon, the time that the sun 
passes the meridian, is a distinct and visible moment, which, with 
proper care and proper instruments, can be exactly defined by 
observation ; not so with midnight, or any other moment, du- 
ring the 24 hours. 

Suppose the right ascension of a star is 8h. 32m. 16s., what time should 
be shown by the astronomical clock, when that star passes the meridian ? 
How are planets and comets distinguished from the fixed stars? By what 
observations? Why do astronomers commence the day at noon ? 



38 ELEMENTARY ASTRONOMY. 



CHAPTER V. 

LATITUDE — DECLINATION — ASTRONOMICAL 
INSTRUMENTS. 

Ix the last chapter we have given a general idea of finding 
the right ascensions of the heavenly bodies — but to give a true 
view or map of the heavens, we must give the declinations also. 

To observe declination, we must have an instrument to 
measure angles, and with it, determine the latitude of the 
place from whence the observations are made. 

The true altitude of the celestial pole is the latitude of the place 
of observation, and primarily, the observation to find this alti- 
tude is the only method of finding the latitude, — but after the 
positions of the heavenly bodies have been established, then 
there are many other methods of finding the latitude. 

As the north pole is but an imaginary point, no star being 
there, we cannot directly observe its altitude. But there is a 
bright star near the pole, called the Polar Stir, which, like 
all other stars in the same region, apparently revolves round 
the pole, and comes to the meridian twice in 24 sidereal hours ; 
once above the pole, and once below it ; and it is evident that 
the altitude of the pole itself must be midway between the 
greatest and least altitudes of the same star, provided the appa- 
rent motion of the star round the pole is really in a circle ; but 
before we examine this fact, we will show how altitudes can be 
taken by the mural circle. 

The mural, or wall circle, is a large metalic circle, firmly 
fastened to a wall, so that its plane shall coincide with the 
plane of the meridian. 

Define the latitude of a place. In the early stages of Astronomy, were 
there many ways of finding latitude ? "When can we find many methods 
of finding latitude ? Is the celestial pole a visible point ? How then can 
we define it ? 



LATITUDE — DECLINATION — INSTRUMENTS. 



39 




A perpendicular line 
through the center, ZiV, 
represents the zenith and 
nadir points ; and at right 
angles to this, through the 
center, is the horizontal 
line, Hh. 

A telescope, Tt, and an 
index bar, li, at right an- 
gles to the telescope, are 
firmly fixed together, and 
made to revolve on the 
center of the mural circle. 

The circle is graduated from the zenith and nadir points, 
each way, to the horizon, from to 90 degrees. 

When the telescope is directed to the horizon, the index 
points, /and i, will be at Z and N, and, of course, show 0° of 
altitude. When the telescope is turned perpendicular to Z, 
the index bar will be horizontal, and indicate 90 degrees of 
altitude. 

When the telescope is pointed toward any star, as in the 
figure, the index points, /and i, will show the position of the 
telescope, or its angle from the horizon, which is the altitude of 
the star. 

As the telescope, and index of this instrument, can revolve 
freely round the whole circle, we can measure altitudes with 
it equally well from the north or the south ; but as it turns 
only in the plane of the meridian, we can observe only meri- 
dian altitudes with it. 

This instrument has been called a transit circle, and, says 
Sir John Herschel, "The mural circle is, in fact, at the same 
time, a transit instrument ; and, if furnished with a proper sys- 
tem of vertical wires in the focus of its telescope, may be used 
as such." 



When the telescope points to a star, how will the instrument show the 
altitude of the star ? Can the telescope move out of the meridian ? 




40 ELEMENTARY ASTRONOMY. 

For a transit instrument, the focus of the eye -piece must be 
furnished with a system of wires, as here represented, "one 
horizontal and five equi-distant threads or wires, " which always 
appear in the field of view, when properly illuminated, by day 
by the light of the sky, by night by that 
of a lamp, introduced by a contrivance not 
necessary here to explain. The place of 
this system of wires may be altered by 
adjusting screws, giving it a lateral (hori- 
zontal) motion ; and it is by this means 
Meridian Wires, brought to such a position, that the middle 
one of the vertical wires shall intersect the line of collimation 
of the telescope, where it is arrested and permanently fastened. 
In this situation it is evident that the middle thread will be a 
visible representation of that portion of the celestial meridian 
to which the telescope is pointed ; and when a star is seen to 
cross this wire in the telescope, it is in the act of culminating, 
or passing the celestial meridian. The instant of this event is 
noted by the clock or chronometer, which forms an indispen- 
sable accompaniment of the transit instrument. For greater 
precision, the moment of its crossing each of the vertical 
threads is noted, and a mean taken, which (since the threads 
are equi-distant) would give exactly the same result, were all 
the observations perfect, and will, of course, tend to subdivide 
and destroy their errors in an average of the whole.' ■ 

To measure altitudes in all directions, we must have another 
instrument, or a modification of this. 

Conceive this instrument to turn on a perpendicular axis 
parallel to ZX, in place of being fixed against a wall; and 
conceive, also, that the perpendicular axis rests on the center 
of a horizontal circle, and on that circle carries a horizontal 
index, to measure azimuth angles. 

This instrument, so modified, is called an altitude and 

How is the meridian made visible ? "What is the use of more than one 
vertical wire? What instrument must always accompany the transit 
instrument ? What is meant by azimuth angles ? 



LATITUDE — DECLINATION — INSTRUMENTS. 4 1 

azimuth instrument, because it can measure altitudes and azi- 
muths at the same time. 

We have before said, that the altitude of the celestial pole 
must be midway between the greatest and least altitude of the 
polar star, provided that star apparently circulates round the pole 
in a circle. To decide that question, all we have to do is to 
measure the direction of the star, east and west of the meridian, 
and compare the amount with the difference between its great- 
est and least altitudes, and if the amount is the same, the appa- 
rent motion is unquestionably circular ; but observation shows 
that the horizontal diameter of the circle is greater than the 
perpendicular diameter. 

Hence, we cannot say that the midway altitude of the polar 
star is the measure of the latitude of the place. But if it is, the 
same kind of observation on other circumpolar stars, must give 
the same latitude. Such observations have been taken, and 
stars at the same distance from the pole gave the same lati- 
tude, and stars at different distances from the pole gave differ- 
ent latitudes ; and the greater the distance of any star from the 
pole, the greater the latitude deduced from it. A star 30 or 35 
degrees from the pole, observed from about the latitude of 40 
degrees, will give the latitude 12 or 15 minutes of a degree 
greater than the pole star. 

Astronomers investigated this subject thoroughly, and exam- 
ined the apparent paths of the stars round the pole, by means 
of the altitude and azimuth instrument, and they were found to 
be not exact circles; but departed more and more from a circle, 
as the star was a greater and greater distance from the pole. 

These curves were found to be somewhat like ovals — the 
longer diameter passing horizontally through the pole — the 

What is the latitude of a place measured by, or what does it correspond 
to ? Do the stars apparently circulate round the pole in perfect circles ? 
What kind of a figure does the motion of a star round the pole appear to 
describe ? What is the position of the longest diameter of these ovals ? 
What half of these ovals more nearly correspond to semicircles, the upper 
or lower ? 

4 



42 



ELEMENTARY ASTRONOMY. 



upper segments very nearly semicircles, and the lower segments 
flattened on their under sides. 

With such evidences before the mind, men were not lonp- 
in deciding that these discrepancies were owing to 

ATMOSPHERICAL REFRACTION. 

It is shown, in every treatise on natural philosophy, that 
light, passing obliquely from a rarer medium into a denser, is 
bent towards a perpendicular to the new medium. 

Now, when rays of light pass, or are conceived to pass, 
from any celestial objects, through the earth's atmosphere to 
an observer, the rays must be bent downward, unless they pass 
perpendicularly through the atmosphere; that is, come from 
the zenith. 

Let AB, CD, 
JEF, &c. represent 
different strata of 
the earth's atmos- 
phere. Let s be a 
star, and conceive 
a line of light to 
pass from the star 
through the vari- 
ous strata of air, 
to the observer, at 
0. When the ray 
of light meets the 
first strata, as EF, it is slightly bent downward ; and as the 
air becomes more and more dense, its refracting power be- 
comes greater and greater, which more and more bends the 
ray. But the direction of the ray, at the point where it meets 
the eye of the observer, will determine the position of the star 
as seen by him. Hence, the observer at will see the star at 
s', when its real position is at s. 

As a ray of light, from any celestial object, is bent down- 




Do lines of light pass through the atmosphere in straight lines 
what direction are the ravs bent ? 



In 



ATMOSPHERICAL REFRACTION. 43 

ward, therefore, as we may see by inspecting the figure, the 
altitude of all the heavenly bodies is increased by reflection. 

This shows that all altitudes, as they come from the instru- 
ment, must be apparent altitudes and not true altitudes, and 
the apparent altitude is always greater than the corresponding 
true altitude, because the body is elevated by refraction. 

If it were not for refraction, the curves round the pole 
would be perfect circles, and the mathematician, by means of 
the altitude and azimuth, which can be taken at any and every 
point of a curve, can determine how much it deviates from a 
circle, and from thence the amount of refraction, at the several 
points. 

By using the refraction thus imperfectly obtained, he can 
correct his altitudes, and obtain his latitude, to considerable 
accuracy. Then, by repeating his observations, he can fur- 
ther approximate to the refraction. 

In this way, by a multitude of observations and computa- 
tions, the table of refraction (which appears among the tables 
of every astronomical work) was established and drawn out. 

The effect of refraction, as we have already seen, is to in- 
crease the altitude of all the heavenly bodies. Therefore, by 
the aid of refraction, the sun rises before it otherwise would, 
and does not set as soon as it would if it were not for refrac- 
tion ; and thus the apparent length of every day is increased 
by refraction, and more than half of the earth's surface is con- 
stantly illuminated. The extra illumination is equal to a zone, 
entirely round the earth, of about 40 miles in breadth. 

As the refraction in the horizon is about 33' of a degree, the 
length of a day, at the equator, is more than four minutes 
longer than it otherwise would be, and the nights four minutes 
shorter. 

At all other places, where the diurnal circles are oblique to 

What is apparent altitude ? What is true altitude ? Which is greatest, 
the apparent or the true altitude of a heavenly body ? What effect does 
refraction have on the time of the sun's rising? What on the length of a 
day? 



44 ELEMENTARY ASTRONOMY. 

the horizon, the difference is still greater, especially if we take 
the average of the whole year. 

In high northern latitudes, the long days of summer are 
very materially increased, in length, by the effects of refrac- 
tion ; and near the pole, the sun rises, and is kept above the 
horizon, even for days, longer than it otherwise would be, 
owing to the same cause. 

Refraction varies very rapidly, in its amount, near the hori- 
zon ; and this causes a visible distortion of both sun and moon, 
just as they rise or set. 

For instance, when the lower limb of the sun is just in the 
horizon, it is elevated, by refraction, 33'. 

But the altitude of the upper limb is then 32', and the re- 
fraction, at this altitude, is 27' 50", elevating the upper limb 
by this quantity. Hence, we perceive, that the lower limb is 
elevated more than the upper ; and the perpendicular diameter 
of the sun is apparently shortened by 5' 10", and the sun is 
distinctly seen of an oval form, which deviates more from a 
circle below than above. 

The apparently dilated size of the sun and moon, when near 
the horizon, has nothing to do with refraction : it is a mere 
illusion, and has no reality, as may be known by applying the 
following means of measurement. 

Roll up a tube of paper, of such a size and dimensions as 
just to take in the rising moon, at one end of the tube, when 
the eye is at the other. After the moon rises some distance 
in the sky, observe again with this tube, and it will be found 
that the apparent size of the moon will even more than fill it. 

When small stars are near the horizon, they become invi- 
sible ; either the refraction enfeebles and dissipates their light, 

What effect does refraction have on the length of a day in high northern 
latitudes ? How much more than half of the earth is enlightened bj the 
sun at any one time ? What effect does refraction have on the apparent 
shape of the sun at rising and setting ? Why should refraction give that 
appearance ? Is the moon apparently larger when near the horizon, than 
when near the zenith ? 



ATMOSPHERICAL REFRACTION- 45 

or the vapors, which are always floating in the atmosphere, 
serve as a cloud to obscure them. 

Having shown the possibility of making a table of refraction 
corresponding to all apparant altitudes, we can now, by apply- 
ing its effects to the observed altitudes of the circumpolar 
stars, obtain the true latitude of the place of observation. 

A table of refraction is to be found in the latter part of this 
volume, and we give a few examples to explain its use. 

1. The apparent altitude of a star was 31° 20', what was its 
true altitude? 

By inspecting the table we find 1' 35" corresponds to the 
apparent altitude 31° 20'. 

Therefore, from - - 31° 20' 00" 
Subtract, - 1' 3i/ 



True altitude required, - 31° 18' 25" 

2. The apparent altitude of the sun's center, was observed to he 
22° 12' 12", what was its true altitude ? 

Apparent altitude, - 22° 12' 12" 

From the table, (Sub.) 2' 22" 



True altitude. - - 22° 9' 50" 

3. The altitude of a star was observed to be 8° 32', what was its 
true altitude ? 

From, - - - , 8° 32' 00" 

Subtract 6' 9" from the table, 6' 9" 



True altitude, at that time, 8° 25' 51" 
f Thus we might add examples without end. 

Let it be borne in mind, that the latitude of any place on the 
earth, is the inclination of its zenith to the plane of the equator ; 
which inclination is equal to the altitude of the pole above the 
horizon. 

What is the inclination of the zenith and the celestial equator equal to ? 



46 ELEMENTARY ASTRONOMY. 

We demonstrate this as follows. Let E represent the earth. 

Now as an obser- 
ver always conceives 
himself to be on the 
topmost part of the 
earth, the vertical 
point, Z, truly and 
naturally represents 
his zenith. Through 
E y draw HE 0, at right angles to EZ ; then HE will rep- 
resent the horizon (for the horizon is always at right angles to 
the zenith). 

Let EQ represent the plane of the equator, and at right 
angles to it, from the center of the earth, must be the earth's 
axis; therefore, EP, at right angles to EQ, is the direction of 
the pole. 

Now the arcs, - - ZP+P 0=90°, 
Also, .... ZP+ZQ=90°, 




By subtraction, - - PO — ZQ—0; 

Or, by transposition, the arc PO=ZQ; that is, the alti- 
tude of the pole is equal to the latitude of the place ; which 
was to be demonstrated. 

In the same manner, we may demonstrate that the arc HQ 
is equal to the arc ZP ; that is, the polar distance of the zenith is 
equal to the meridian altitude of the celestial equator. Now, we 
perceive, that by knowing the latitude, we know the several 
divisions of the celestial meridian, from the northern to the 
southern horizon, namely, OP, PZ, ZQ, and QH. 

By observing the extrenrpe altitudes of the circumsolar stars, and 
correcting such altitudes for refraction, the half sum of the true ex- 
treme altitudes of any one star, will be the latitude of the place of 
observation. 

What place is the earth ? s axis perpendicular to ? What is the altitude 
of the pole equal to ? What is the polar distanpe of Ihe zenith equal to "? 



ATMOSPHERICAL REFRACTION". 47 

We give an example. 
The greatest observed altitude of the polar star, 41° 37' 
Refraction, - - - - - 1' 5" 



True altitude, ... - 41 35' 55" 

The least observed altitude of the same star, 38° 39' 15" 
Refraction, - - - - - 1' 12" 



Least true altitude - - 38° 38' 3' 

Greatest true altitude. - - - 41° 35' 55'' 



Sum, 80° 13' 58" 



Half sum latitude - - - 40° 6' 59" 

We might take any other circumpolar star, as well as the 
pole star — but the pole star is the least liable to error, because 
of the smaller circle it describes. 

We are now prepared to observe and record the declination 
of the stars, or any heavenly body. 

The declination of a star, or any celestial object, is its meridian 
distance from the celestial equator. 

To determine the declination of a star, we must observe its 
meridian altitude (by some instrument, say the mural circle,) 
and correct the altitude for refraction, the difference will be 
the star's true altitude. 

If the true meridian altitude of the star is less than the meridian 
altitude of the celestial equator, then the declination of the star is 
south. If the meridia.n altitude of the star is greater than the meri- 
dian altitude of the equator, then the declination of the star is 
north. 

These truths will be apparent by merely inspecting the last 
figure. 

How is the latitude of a place originally determined ? What is under- 
stood by the declination of a star ? When the declination of a star is 0, 
how far is it from the pole ? 



48 ELEMENTARY ASTRONOMY. 

EXAMPLES. 

1. Suppose an observer in the latitude of 40° 12' 18" north, 
observes the meridian altitude of a star, from the southern horizon, 
to be 31° 36' 37"/ what is the declination of that star ? 

From 90° 0' 00" 

Take the latitude, - - - 40° 12' 18" 



Diff. is the meridian alt. of the equator, 49° 47' 42" 

Alt. of star, 31° 36' 37" 
Refraction, 1' 32" 



True altitude, 31° 35' 5" - - 31° 35' 5" 



Declination of the star, south, - - 18° 12' 37" 

2. The same observer finds the meridian altitude of another 
star, from the southern horizon, to be 79° 31' 42" ; what is the de- 
clination of that star? 

Observed altitude, 79° 31' 42" 

Refraction, - 11 



True altitude, - - - - 79 31 31 

Altitude of equator, - - - - 49 47 42 



Star's declination, north, - - 29° 43' 49" 

3. The same observer, and from the same place, finds the meri- 
dian altitude of a star, from the northern horizon, to be 51° 29' 
53" ; what is the declination of that star? 

Observed altitude, 51° 9.9' 53" 

Refraction, - 46 

True altitude of star, - 
Altitude of pole (or latitude), 

Star from the pole (or polar dist.), 
Polar dist., from 90°, gives decl. north, 

How do you find the meridian altitude of the equator ? When a star 
comes to the zenith, how can we find its declination ? 



51 


29 


7 


40 


12 


18 


11 


16 


49 


78° 


43' 


11' 



ATMOSPHERICAL REFRACTION. 49 

In this way the declination of every star in the visible 
heavens can be determined. 

In Chapter IV, we explained how to obtain the difference 
of the right ascension of the stars, and this, with the declination, 
will enable us to mark down the position of the stars, on a globe, 
and thus give a true representation of the appearance of the hea,vens. 

Quite a region of stars exists around the south pole, which 
are never seen from these northern latitudes ; and to observe 
them, and define their positions, Dr. Halley, Sir John Her- 
schel, and several other English and French astronomers, 
have, at different periods, visited the southern hemisphere. 
Thus, by the accumulated labors of many astronomers, we at 
length have correct catalogues of all the stars in both hemis- 
pheres, even down to many that are never seen by the naked 
eye. 

There are several constellations in the southern regions, 
worthy of notice — the Southern Cross and the Magellan Clouds. 
The Southern Cross very much resembles a cross ; so much so, 
that any person would give the constellation that appellation. 
Its principal star is, in the right ascension, 12h. 20 m., and 
south declination 33°. 

The Magellan Clouds were at first supposed to be clouds, 
by the navigator Magellan, who first observed them. They 
are four in number ; two are white, like the Milky Way, and 
have just the appearance of little white clouds. They are 
nebula. The other two are black— extremely so — and are 
supposed to be places entirely devoid of all stars ; yet they are 
in a very bright part of the Milky Way — right ascension 
10 h. 40 m., declination 62° south. 

Can -we see all the stars in the heavens from the northern latitudes ? 
What is said of the stars in the southern hemisphere ? What are the Ma- 
gellan Clouds ? Have they all a similar appearance ? 
5 



60 ELEMENTARY ASTRONOMY. 

CHAPTER VI. 
SCIENTIFIC METHODS OF FINDING PARTICULAR STARS. 

Among our tables will be found a catalogue of one hundred 
of the principal stars, inserted for ike purpose of teaching the 
learner the scientific method of defining the stars. 

To have a clear understanding of the method we are about 
to explain, we must again consider that right ascension is 
reckoned from the equinox, eastward along the equator, from 
Oh. to 24 hours. When the sun comes to the equator, in 
March, its right ascension is 0; and from that time its right 
ascension increases about four minutes in a day, through the 
year, to 24 hours ; and then it is again at the equinox, and the 
24 hours are dropped. 

But whatever be the right ascension of the sun, it is appa- 
rent noon when it comes to the meridian ; and the more east- 
ward a body is, the later it is in coming to the meridian. 
Thus : Jf a star comes to the meridian at two o'clock in the after- 
noon (apparent time), * it is because its right ascension is two 
hours greater than the right ascension of the sun. 

Therefore, if from the right ascension of a star we subtract 
the right ascension of the sun, the remainder will be the appa- 
rent time for that star to come to the meridian. 

If we put (R^fr) to represent the star's right ascension, and 
(i?®) to represent that of the sun, and T to represent the ap- 
parent time that the star passes the meridian, then we shall 
have the following equation : 

By transposition R^—B^-\-T; 

•We will explain the difference between apparent time, and common 
clock time, in a future chapter. The difference is never 17 minutes, com- 
monly much less. 

How do you find the right ascension of a star, or any heavenly body ? 



METHOD OF FINDING PARTICULAR STARS. 



51 



That is, to find the right ascension of a star, (or any heavenly- 
body), Add the right ascension of the sun to the apparent time the 
body is observed to pass the meridian. 

The right ascension of the sun is given, in the Nautical 
Almanac (and in many other almanacs), for every day in each 
year, when the sun is on the meridian of Greenwich ; but 
many of the readers of this work may not have such an alma-j 
nac at hand, and for their benefit, we give the right ascension 
for every fifth day of the year 1846, in the following table, which 
will show the right ascension for the same day in any other year 
within three minutes of time during the present century, and 
this will be sufficiently accurate to illustrate the principle. 



SUN'S RIGHT ASCENSION FOR 1846. 



Day 














of 
Mo. 


January. 


February. 


March. 


April. 


May. 


June. 




h. m. s. 


h. m. s. 


h. m. s. 


h. m. s. 


h. m. s. 


h. m. s. 


1 


18 46 52 


20 59 11 


22 48 17 


41 52 


2 23 6 


4 35 48 


5 


19 4 30 


21 15 22 


23 3 12 


56 26 


2 48 25 


4 52 12 


10 


19 26 21 


21 35 18 


23 21 40 


1 14 43 


3 7 47 


5 12 50 


15 


19 47 57 


21 54 54 


23 40 


1 33 6 


3 27 24 


5 33 34 


20 


20 9 17 


22 14 12 


23 58 14 


1 51 38 


3 47 15 


5 54 22 


25 


20 30 19 


22 33 14 


16 25 


2 10 22 


4 7 20 


6 15 10 


30 


20 51 




34 36 


2 29 17 


4 27 18 


6 35 55 


Day. 
of 
Mo. 


July. 


August. 


September. 


October. 


November. 


December. 


h, m. s. 


h. m. s. 


h. m. s. 


h. m. s. 


h. m. s. 


h. m. s. 


1 


6 40 4 


8 44 55 


10 41 


12 29 4 


14 25 16 


16 29 1 


5 


6 56 34 


9 23 


10 55 29 


12 43 36 


14 41 2 


16 46 23 


10 


7 17 5 


9 19 29 


11 13 30 


13 1 54 


15 1 5 


17 8 17 


15 


7 37 25 


9 38 21 


11 31 28 


13 20 24 


15 21 28 


17 30 22 


20 


7 57 33 


9 56 60 


11 49 25 


13 39 8 


15 42 14 


17 52 33 


25 


8 17 28 


10 15 27 


12 7 24 


13 58 9 


16 3 19 


18 14 46 


30 


8 37 7 


10 33 44 


12 25 27 


14 17 27 16 24 43 


18 36 57 



To obtain sufficient data to apply the preceding rule, the 
observer should adjust his watch to apparent time, that is, 
apply the equation of time, or in other words, see that his watch 
shows 12 o'clock when the sun is on the meridian, and he 
must know the- direction of the meridian from which he takes 
the observations. In short, by the range of definite objects, he 

When is it apparent noon ? 



52 ELEMENTARY ASTRONOMY. 

Diust be able to decide, within two or three minutes, when a 
celestial body is on the meridian. 

Thus being all prepared, we give a few 

EXAMPLES. 

1 . Being in latitude about 40° north-, and on the 20th of May, at 
9A. 27/n-. in the evening, apparent time, I observed a lone bright star, 
of about the Id magnitude, on the meridian. I had no instrument 
to measure its altitude, but I simply judged the altitude to be about 
42° from the southern horizon. What star was this ' 

We determine it thus: 

On the 20th of May, at 9 in the evening, the right ascension 
of the sun cannot be far from, - - - - 3h 49m 

To this add the apparent time of passing the merid. 9h 27m 



The sum is the right ascension of the star. - 13h 16m 
By inspecting the catalogue of stars, we find the right as- 
cension of Spica is registered at 13h 17m 8s., therefore it is 
more than probable that the star observed was Spica. 

To make it sure, we find that the declination of Spica in the 
catalogue, is 10° 21' 35" south: but in latitude 40° north, the 
meridian altitude of the celestial equator must be 50°; and any 
stars south of that must have a less altitude. Therefore, the 
meridian altitude of Spica must be 50°, less 10° 21', or 39° 
39'; but the star I observed, I simply judged to have had an 
altitude of 42°. It is very possible that I should err, in alti- 
tude, two or three degrees ;* but, it is ?iot possible that the star I 

*Ten or twenty degrees, near the horizon, is apparently a much larger 
space than the same number of degrees near the zenith. Two stars, when 
near the horizon, appear to be at a greater distance asunder than when 
their altitudes are greater. The variation is a mere optical illusion ; for, 
by applying instruments to measure the angle in the different situations, 
we nnd' it the same. Unless this fact is taken into consideration, an ob- 
server will always conceive the altitude of any object to be greater than it 
really is, especially if the altitude is less than 45 degrees. 

If a star was obseived to pass the meridian at lOh 12m in the evening, 
when the sun's right ascension was 2h 5m., what must have been the 
right ascension of that star? 



METHOD OF FINDING PARTICULAR STARS. 53 

observed should be any other star than Spica; for there is no 
other bright star near it. This is one of the lunar stars. 

Being now certain that this star is Spica, I can observe it in 
relation to its appearance — the small stars that are near it, and 
the clusters of stars that are about it — or the fact, that no re- 
markable constellation is near it. In short, I can so make its 
acquaintance as to know it ever after ; but I am unable to 
convey such acquaintance to others by language ; true know- 
ledge, in this particular, demands personal observation. 

2. On the Sd of July, at 9h 30m. apparent time, in the evening, 
in latitude 39° north, and longitude about 75° west, a star of the 
first magnitude was observed to %)ass the meridian. The star was of 
a deep red color, and, as near as my judgment could decide, its alti- 
tude was between 25° and 30°. Two small stars were near it, and a 
remarkable cluster of smaller stars were west and northwest of it, 
at the distances of 5°, 6°, or 7°. What star was this? 

Sun's right ascension at the time, - - 6h 50m 
Apparent time the star passed meridian, - 9h 30m 



Right ascension of the star, - - - 16h 20m 

By inspecting the catalogue of stars, I find Antares to have a 
right ascension of 16h. 20m. 2s. and a declination of 26° 4', 
south. 

In the latitude mentioned, the meridian altitude of the celes- 
tial equator must be - - - - 51° 0' 

Objects south of that plane must be less, hence (sub.) 26° 54' 



Meridian altitude of Antares, in lat. 39° north, 24° 56' 

As the observation corresponds to the right ascension of An- 

tares (as nearly as possible, considering errors in observations, 

and probably in the watch), and as the altitudes do not differ 

many degrees (within the limits of guess work), it is certain 

Can any one recognize particular stars in the heavens without personal 
observation ? In the 2d example, how do we know that the star observed 
was Antares ? What is the right ascension of Antares ? 



64 ELEMENTARY ASTRONOMY. 

that the star observed was Antares. By its peculiar red color, 
and the remarkable clusters of stars surrounding it, I shall be 
able to recognize this star again, without the trouble of direct 
observation. 

3. On the night of the 20th of June, in latitude 40° north and 
longitude 75° west, at \h Mm. past midnight, apparent time, a star 
of the first magnitude was observed to pass the meridian : two other 
stars of about the third magnitude were within 3° of it ; the three stars 
forming nearly a right line north and south ; the altitude of the 
principal stars from the south was about 60°. What star was it? 

In these examples, the time must be reckoned from noon to 
noon again, 24 hours, and if the sum of any addition exceeds 
24 hours, the excess only must be taken. 

In this example, lh 47m after midnight must be written 13h 
47m. 

The longitude of 75° west, also adds 5 hours to the Green- 
wich time, hence the time that this star passed the meridian, 
was June 20th, the 18th hour of that day, within 6 hours of the 
21st of June. To this time we compute the sun's right ascen- 
sion. 

Sun's right ascension at the time the star was on the meri- 
dian could not be far from, - - - - 5h 58m 
To this add, 13 47 



Sum, is the right ascension of the star, - 19h 45m. 

By inspecting the catalogue of stars, we find the right as- 
cension of Altair 19 h. 43 m. 15s., and its declination 8° 27' N. 
In latitude 40° N., the declination of 8° 27' JSF. will give a me- 
ridian altitude of 55° 27' ; and, in short, I know the star ob- 
served must be Altair, and the two other stars, near it, I recog- 
nize in the catalogue. 

What is the color of Antares ? Is there a cluster of stars near Antares, and 
in what direction ? Suppose the time is after midnight, how do you reckon 
it ? If the sum found by adding the right ascension of the sun to the time a 
body passed the meridian, should exceed 24 hours, what would you do ? 



METHOD OF FINDING PARTICULAR STARS. 65 

By taking these observations, any person may become ac- 
quainted with all the principal stars, and the general aspect of 
the heavens ; but no efforts, confined merely to the study of 
books, will accomplish this object. 

The rule here used is not solely confined to the stars, it is 
applicable to any heavenly body, moon, comet, or planets, and if 
the foregoing examples are understood, the reader will have a 
good general idea how the right ascension of the moon, and 
planets, are from time to time, determined by observation. 

The time of passing the meridian is relatively but another 
term for right ascension, and if observations are made on any 
bright star, and no corresponding star is to be found in the 
catalogue, such a star would probably be found to be a planet, 
and if a planet, its right asension will change. 

WE MAY NOW REVERSE THE PROBLEM. 

Suppose that we wish to find any particular star, for example, 
Aldebaran. 

It is a clear star light night, January 19th, the sun's right 
ascension by the Nautical Almanac, I find approximately to 
be about 20h. 5m., and in the catalogue of stars I find the 
right ascension of Aldebaran to be 4h. 27m. disregarding the 
seconds. 

The equation, R% — E^=T is general, and shows us that 
we must subtract the right ascension of the sun from the right 
ascension of the star, and the remainder is the apparent time 
that the star comes to the meridian. To render the subtrac- 
tion possible, we must in some cases increase the right ascen- 
sion of the star by 24 hours. 

h. m. 
From i^-+24 hours - - - 28 27 

Subtract J$m 20 5 



Aldebaran on the meridian (Jan. 19th), - 8 22 

How can we find the right ascension of the moon, or a planet, by obser- 
vation ? How do we find the time when any particular star will pass the 
meridian ? 



66 ELEMENTARY ASTRONOMY. 

This shows, that if the stars are visible on the 19th of Jan- 
uary, of any year, and we look along the meridian at about 20 
minutes after 8 in the evening, we shall certainly see Aldebaran. 

Suppose it the 10th of March, of any year, and a learner 
wishes to be sure of finding the star Sirius. 

He must inspect the catalogue of stars, and he will find its 
right ascension to be 6h. 38m. ; and by the table on page 51, 
or better, by a Nautical Almanac, he will find the right ascen- 
sion of the sun, on the 10th of March, to be not far from 23h. 

22m., therefore 

h. m. 
From R^ 6h. 38m.+24h. - 30 38 

Subtract - - - 23 22 



Sirius on the meridian, March 10th, 7 16 apparent time. 

Now, if on that day of the year, at about 16 minutes past 7, 
apparent time in the evening, we observe the heavens, we shall 
certainly see Sirius in a southern direction, and by taking into 
consideration our latitude and the declination of the star, we 
can form a very correct estimate of its altitude, and we could 
as readily find the star as we could find the moon. 

In this manner we may find when any particular star will come 
to the meridian, and take that time to observe it. Speaking loosely, 
the same star comes to the meridian at the same hour and 
minute, sidereal time, througout the year, but at different times, 
on different days, by the solar clock. On account of the sun 
changing its right ascension from day to day, sidereal time is in 
fact right ascension. 

Do the stars come to the meridian at the same time throughout the year, 
by the sidereal clock ? "Why then do they vary by the solar or common 
clock ? 



FIGURE AND MAGNITUDE OF THE EARTH. 57 

CHAPTER VII. 

PLANETS — FIGURE AND MAGNITUDE OF THE EARTH. 

In the preceding chapter, we have been careful to impress 
the fact, that the great mass of the stars pass the meridian at 
regular intervals of time, and that the same star will pass the 
meridian at intervals of 24 sidereal hours, which corresponds to 
23h. 56m. 4.09s. of mean solar time. 

If sidereal time of 24h. between the passage of the same star 
over the meridian is taken for the standard measure of time, 
then the mean intervals between two consecutive passages of 
the sun across the meridian is 24h. 3m. 56.5554s. 

We say mean interval, because this interval is not always 
the same, and not being the same, gives rise to the equation of 
time. The cause of this inequality, and consequently the cause 
of the equation of time, will be examined hereafter; the fact was 
first observed by noting the passage of the sun across the meri- 
dian, in comparison with a well regulated sidereal clock. 

All those stars that pass the meridian at equal intervals ot 
time, and always at the same altitude, if observed from the 
same station, are called and must be in fact, fixed stars, but the 
sun coming to the meridian at unequal intervals of time, and at 
different altitudes from the horizon, shows that it is not a fixed 
body. 

When we compare the times of the moon passing the meri- 
dian, with the astronomical clock, we are very forcibly struck 
with the irregularity of the interval. 

The least interval between two successive transits of the 
moon (which may be called a lunar day), is observed to be 

What has the author been careful to impress, in the previous chapter ? 
What astronomical interval is always the same ? Does the sun come to 
the meridian at equal intervals of time ? To what does this give rise ? 



53 ELEMENTARY ASTRONOMY. 

about 24h. 42m. ; the greatest, 25h. 2m, ; and the mean, or 
average, 24h. 54m., of mean solar time. 

These facts show, conclusively, that the moon is not a fixed 
body, like a fixed star, for then the interval would be 24 hours 
of sidereal time. 

But as the interval is always more than 24 hours, it shows 
that the general motion of the moon is eastward, among the 
stars, with a daily motion varying from 10-J to 16 degrees, 
traveling, or appearing to travel, through the whole circle of 
the heavens (360°) in a little more than 27 days. 

Thus these observations, however imperfectly and rudely 
taken, at once disclose the important fact, that the sun and 
moon are in constant change of position, in relation to the 
stars, and to each other ; and we may add, that the chief ob- 
iect and study of astronomy, is, to discover the reality, the 
causes, the nature, and extent of such motions. 

Besides the sun and moon, several other bodies were noticed 
as coming to the meridian at very unequal intervals of time, 
intervals not differing so much from 24 sidereal hours as the 
moon, but, unlike the sun and moon, the intervals were some- 
times less, sometimes greater, and sometimes equal to 24 side- 
real hours. 

These facts show that these bodies have a real, or apparent 
motion, among the stars, which is sometimes westward, some- 
times eastward, and sometimes stationary ; but, on the whole, 
the eastward motion predominates ; and, like the sun and 
moon, they finally perform revolutions through the heavens 
from west to east. 

Only four such bodies (stars) were known to the ancients, 
namely, Venus, Mars, Jupiter, and Saturn. 

These stars are a portion of the planets belonging to our solar 
system, and, by subsequent research, it was found that the 
Earth was also one of the number. As we come down to 
more modern times, several other planets have been discovered, 

What direction does the moon move in respect to the fixed stars ? How- 
many degrees does it move in a day ? In how many days will it make a 
revolution ? What other wandering bodies were observed by the ancients ? 



FIGURE AND MAGNITUDE OF THE EARTH. 



59 



namely Mercury, Uranus, Vesta, Juno, Ceres, Pallas, and very 
recently, Neptune, Iris, Hebe, Flora, Astrea, and one or two 
others of no moment to record in a work like this. 

We here mention the names of these planets in the order of 
their discovery, and not in the order in which they revolve in 
the system, for as yet we have no definite idea of a planet or a 
planetary system. In the tables, they will be found in their 
proper order in reference to the center of the system. 

It is unreasonable and unnatural to suppose that the appa- 
rent motions of these wandering stars are their real motions, as 
viewed from a stationary point; such irregularities in apparent 
motions can only be accounted for, on the supposition that the 
observer, on the earth, that is, the earth itself, is in motion as 
well as the planets. 

The ancients, taking the first impressions of their senses, 
supposed the earth to be a plane, and the principal object in the 
universe, and under this idea the planetary motions were inex- 
plicable; but we shall not pretend to explain the slow process 
of knowledge which gradually melted away this erroneous im- 
pression, we shall simply bring forth science, as it is now 
known to exist, and therefore we must now consider the 

FIGURE AND MAGNITUDE OP THE EARTH. 

The greater portion of the surface of the earth is water, and 
the surface of water is every where convex, as any observer may 
convince himself who takes the opportunity to do so. In 
coming in from sea, the high land, back in the country, is seen 
before the shore, which is nearer to the observer ; the tops of 
trees, and the tops of towers, are seen before their bases. Tf 



&SSL 



Is it probable that very irregular motions, such as we observe in the 
planets, are real motions ? Did the ancients suppose the earth to be a 
plane ? How do vre know" that it is not a plane ? 



60 ELEMENTARY ASTRONOMY. 

the observer is on shore, viewing an approaching vessel, he 
sees the topmast first ; and from the top, downward, the vessel 
gradually comes in view. These facts are sufficiently illustra- 
ted by the adjoining figure. 

One of the most striking observations of this kind, is made 
in the Mediterranean sea. On the island of Minorca, near its 
center, stands Mount Toro, and on the very vertex of the moun- 
tain stands a Monastery, three stories high. 

On approaching the island from any direction, in moderate 
and clear weather, the first object that comes to view is the top 
of the Monastery, and approaching nearer, the upper story with 
its windows, becomes distinctly visible — continuing to ap- 
proach, the whole building gradually becomes visible, standing 
apparently alone on the surface of the sea. Then the mountain 
itself appears to rise, and finally, the island and shores around. 
Similar observations are made every day, on every sea, and on 
every portion of the earth, which shows to a demonstration 
that the earth is convex on every part, hence it must be a globe 
or sphere, or nearly so. 

In addition to this, the earth has been circumnavigated many 
times, and navigators make their computations on the supposi- 
tion that the earth is a sphere, and this supposition, at all 
times corresponding to fact, settles the question. 

To this, we will simply call to mind the fact, that the shadow 
of the earth, on the moon, in eclipses of the moon, is always 
circular, which could not always be the case if the earth had 
any other shape than that of a sphere. 

On the supposition that the earth is a sphere, there are sev- 
eral methods of measuring it, without the labor of applying the 
measure to every part of it. The first, and most natural 
method (which we have already mentioned), is that of measu- 
ring any definite portion of the meridian, and from thence 
computing the value of the whole circumference. 

What is said of the Monastery on the island of Minorca ? What is said 
of the shadow of the earth ? If the earth is spherical, how can we measure 
it, without measuring entirely round ? 



FIGURE AND MAGNITUDE OF THE EARTH. 61 

Thus, if we can know the number of degrees, and parts of a 
degree, in the arc AB, and then measure the distance in miles, 
we in fact virtually know the whole circumference; for what- 
ever part the arc AB is of 360 degrees, the same part, the 
number of miles in AB, is of the miles in the whole circum- 
ference. 

That is, as the arc AB is to the whole circumference 360°, so is 
the number of miles in AB to the number of miles in the circum- 
ference. 

To find the arc AB, the latitude of the two points, A and B, 
must be very accurately taken, and their difference will give 
the arc in degrees, minutes, and seconds. Now AB must be 
measured simply in distance, as miles, yards, or feet; but this is 
a laborious operation, requiring great care and perseverance. 
To measure, directly, any considerable portion of a meridian, is 
indeed impossible, for local obstructions would soon compel a 
deviation from any definite line ; but still the measure can be 
continued, by keeping an account of the deviations, and redu- 
cing the measure to a meridian line. 

When we know the hight of 
a mountain, as represented in 
this figure, and at the same 
time know the distance of its 
visibility over the surface of 
the earth ; that is, know the 
line MA; then we can com- 
pute the line MC, by a simple 
theorem in geometry ; thus, 
CMXMB=(AM)* ; 
(AM) 2 




Or, CM= 



MB 



Now as the right hand mem - 



How do we find the arc AB ? How do we find the length of the arc in 
miles or feet ? What rule have we to find the diameter of the earth, when 
•we know the hight of a mountain, and the distance of the visible horizon 
therefrom ? 



62 ELEMENTARY ASTRONOMY. 

ber of this equation is known, CM is known ; and as part of it 
(MB) is already known, the other part, BC, the diameter of 
the earth, thus becomes known. 

This method would be a very practical one, if it were not for 
the uncertainty and variable nature of refraction near the 
horizon ;* and for this reason, this method is never relied 
upon, although it often well agrees with other methods. As 
an example under this method, we give the following : 

A mountain, two miles in perpendicular hight, was seen 
from sea at a distance of 126 miles. If these data are correct, 
what then is the diameter of the earth ? 

Solution: MC=^-^- = 63 XI 26 = 7938. £C = 7936. 

This same geometrical theorem serves to compute the dip of 
the horizon. The true horizon is at right angles from the zenith ; 
but the navigator, in consequence of the elevation of his vessel, 
can never use the true horizon ; he must use the sea offing, 
making allowance for its dip. If the navigator's eye were on a 
level with the sea, and the sea perfectly stable, the true and 
apparent horizon would be the same. But the observer's eye 
must always be above the sea ; and the higher it is, the greater 
the dip ; and the amount of dip will depend on the hight of the 
eye, and the diameter of the earth. The difference between 
the angle AMC, and a right angle (which is equal to the 
angle ABM), is the measure of the dip corresponding to the 
hight BM. 

For the benefit of navigators, a table has been formed, show- 
ing the dip for all common elevations. 

No one should object to considering the earth a sphere, 
because its surface is diversified with mountains and valleys, 
for the highest mountain on the earth is not so large, compared 

*Sometirnes a distant object over sea appears distinctly visible, and at 
other times appears depressed below the horizon. 

What objection is there to the last mentioned method of measuring the 
earth ? What is the dip of the horizon ? If the observer's eye were down 
on the level of the sea, would there be any dip ? 



FIGURE AND MAGNITUDE OF THE EARTH. 63 

to the earth itself, as a fine grain of sand is compared to a 
globe of 18 inches in diameter. No one objects to calling an 
orange round, because of the roughness of its external surface. 

After correct views were entertained, as to the magnitude 
of the earth, and its revolution on an axis, philosophers con- 
cluded that its equatorial diameter might be greater than its 
polar diameter ; and investigations have been made to decide 
that fact. 

If the earth were exactly spherical, it is plain that the cur- 
vature over its surface would be the same in every latitude ; 
but if not of that figure, a degree would be longer on one part 
of the earth than on another. "But," says Herschel, "when 
we come to compare the measures of meridianal arcs made in 
various parts of the globe, the results obtained, although they 
agree sufficiently to show that the supposition of a spherical 
figure is not very remote from the truth, yet exhibit discord- 
ances far greater than what we have shown to be attributable 
to errors of observation ; and which render it evident that the 
hypothesis, in strictness of its wording, is untenable. Without 
troubling the reader with the details of actual measurement, 
which have been made from time to time with all care and 
precision, it is sufficient to state that the measured length of a 
degree increases with the latitude, being greatest near the poles 
and least near the equator, giving ^he following magnitude of 
the earth : 

Greatest, or equatorial diameter, 7924.65 miles. 
Least, or polar diameter, - 7899.17 
Diff. or polar compression, - 26.48 

The proportion of the diameters is very nearly that of 298 to 
299, and their diff. 2t>9-°fthe greater, or a very little over 
g-^,. The shape of the earth, thus ascertained by actual meas- 
urement, is just what theory would give to a body of water 
equal to our globe, and revolving on an axis in 24 hours ; and 

Is the earth exactly spherical, aside from the roughness of its surface? 
How was the shape of the earth determined ? What is the length of the 
equatorial diameter ? What of the polar ? 




G-* ELEMENTARY ASTRONOMY. 

this has caused many philosophers to suppose that the earth 
was formerly in a fluid state. 

If the earth were a sphere, a plumb line at any point on its 
surface would tend directly towards the center of gravity of 
the body ; but the earth being an ellipsoid, or an oblate spheroid, 
and the plumb lines, being perpendicular to the surface at any 
point, do not tend to the center of gravity of the figure, but to 
different points, as represented in the figure. 

The plumb line at H tends to F, 
yet the mathematical center, and 
center of gravity of the figure, is 
at E. So at /, the plumb line 
tends to the point G; and as the 
length of a degree at A, is to the 
length of a degree at H, so is A G 
to HF. If, however, a passage 
were made through the earth, and a body let drop through it, 
the body would not pass from / to G: its first tendency at / 
would be toward the point G; but after it passed below the 
surface at /, its tendency would be moi-e and more toward the 
point F, the center of gravity ; but it would not pass exactly 
through that point, unless dropped from the point A, or the 
point C. 

If the earth were a perfect and stationary sphere, the force 
of gravity, on its surface, would be everywhere the same ; but, 
it being neither stationary, nor a perfect sphere, the force of 
gravity, on the different parts of its surface, must be different. 
The points on its surface, nearest its center of gravity, must 
have more attraction than other points more remote from the 
center of gravity ; and if those points which are more remote 
from the center of gravity have also a rotary motion, there will 
be a diminution of gravity on that account. 

What caused philosophers to suppose that the earth's equatorial diame- 
ter was greater than its polar diameter ? Does the plumb line always tend 
towards the mathematical center of the earth ? Does it always tend per 

pendicularly to the surface of still water ? 



FIGURE AND MAGNITUDE OF THE EARTH. 65 

Let A B in the figure, represent the equatorial diameter of 
the earth, and CD the polar diameter ; and it is obvious that 
E will be the center of gravity, of the whole figure, and that 
the force of gravity at C and D will be greater than at any 
other points on the surface, because EC, or ED, are less than 
any other lines from the point E to the surface . The force of 
gravity will be greatest on the points C and D, also, because 
they are stationary : all other points are in a circular motion; 
and circular motion has a tendency to depart from the center 
of motion, and, of course, to diminish gravity. The diminution 
of the earth's gravity by the rotation on its axis, amounts to 
its 2-J-^th part* at the equator. By this fraction, then, is the 
weight of the sea about the equator lightened, and thereby 
rendered susceptible of being supported at a higher level than 
at the poles, where no such counteracting force exists. 

It is this centrifugal force itself that changed the shape of 
the earth, and made the equatorial diameter greater than the 
polar. Here, then, we have the same cause, exercising at once 
a direct and an indirect influence. Owing to the elliptic form 
of the earth, and independently of the centrifugal force, its 
attraction ought to increase the weight of a body, in. going 
from the equator to the pole, by nearly its 5-9-0-th part; which, 
together with the ^-^th part, due from centrifugal force, make 
the whole quantity yl^-th part; that is, 194 pounds pressure at 
the equator, will press with a force of 195 pounds when carried 
to the poles, which corresponds with the result of observations 
deduced from the vibrations of pendulums. 

The form of the earth is so nearly a sphere, that it is con- 
sidered such, in geography, navigation, and in the general 
problems of astronomy. 

*For the computation which brings this result, see the university edition 
of Astronomy. 

Give two distinct reasons why the force of attraction is greater at the 
poles than at the equator? In what proportion do bodies increase in 
weight on being carried from the equator to the poles ? 
G 



66 



ELEMENTARY ASTRONOMY. 



The average length of a degree is 69|- English miles ; and, 
as this number is fractional, and inconvenient, navigators have 
tacitly agreed to retain the ancient, rough estimate of sixty- 
miles to a degree ; calling the mile a geographical mile. There- 
fore, the geographical mile is longer than the English mile. 

As all meridians come together at the pole, it follows that a 
degree, between the meridians, will become less and less as 
we approach the pole ; and it is an interesting problem to trace 
the law of decrease. 

This law will become apparent, by inspecting the figure in 
the margin. 

Let EQ represent a degree, on 
the equator, and EQC& sector on 
the plane of the equator, and of 
course EC is at right angles to the 
axis CP t » Let DEI be any plane 
parallel to EQC; then we shall 
have the following proportion ; 
EC : PI : : EQ : DF. 

In trigonometry, EC is known as the ra^jmis of the sphere ; 
DI as the cosine of the latitude of the p#mt D (the numerical 
values of sines and cosines, of all arcs, are given in trigonome- 
trical tables): therefore we have the following rule, to compute 
the length of a degree between two meridians, on any parallel 
of latitude: 

Rule. — As radius is to the cosine of the latitude, so is the 
length of a degree on the equator, to the length of a parallel degree 
in that latitude. 

We give the following as an example, although pupils will 
not, and cannot fully comprehend it, unless they are acquainted 
with trigonometry. 




What is the average length of a degree on the earth ? What is the 
difference between an English and a geographical mile ? By what rule do 
two meridians approach each other between the equator and the poles ? 



FIGURE AND MAGNITUDE OF THE EARTH. 67 

Calling a degree, on the equator, 60 miles, what is the 
length of a degree of longitude, in latitude 42°? 

SOLUTION BY LOGARITHMS. 

As radius (see tables), .... 10.000000 

Is to cosine 42° (see tables), - - - 9.871073 

So is 60 miles (log.), - - 1.778151 



To 44 I V<r . miles, - Am. - - 1.649224 

At the latitude of 60°, the degree of longitude is 30 miles ; 
the diminution is very slow near the equator, and very rapid 
near the poles. 

In navigation, the DE's are the known quantities obtained 
by the estimations from the log line, etc. ; and the navigator 
wishes to convert them into longitude, or, what is the same 
thing, he wishes to find their values projected on the equator, 
and he states the proportion thus : 

DI : EC : : DF : EQ; 
That is, as cosine of latitude, is to radius, so is departure, to differ- 
ence of longitude. 

If we take one mile, (either the English or the Nautical 
mile), for the distance between two meridians on the equator; 
the distance between the same two meridians in any latitude 
will be expressed by the cosine of that latitude in any table of 
natural cosines.* 

Thus, Inspecting a table of natural cosines we find that in 
lat. 25° the cosine is 0.906. That is, the distance of one 
mile on the equator, corresponds to the parallel distance of 
.906, 25 degrees distant from the equator. Or 10 miles on the 
equator corrresponds, to 9. T §^ miles in lat. 25°. In Naviga- 
tion, the distance on the equator is called difference of longi- 
tude, and the corresponding distance is called departure. 

We might have taken any other latitude for an example as 
well as 25°. Thus, the decimal cosine of any latitude corresponds 
to one mile on the equator. 

*Such a table is to be found, between pages 21 and 65, of our tables, 
and bound in each of the three volumes, of Robinson's Mathematics, viz. 
In the Geometry, the Surveying and Navigation, and in the Math.^mntieal 
Operations. 



68 



ELEMENTARY ASTRONOMY. 



SECTION II. 

DESCRIPTIVE ASTRONOMY 



CHAPTER I. 



FIRST CONSIDERATIONS AS TO THE DISTANCES OF THE HEAVENLY 
BODIES. — LUNAR PARALLAX AND DISTANCE TO THE MOON. 



Hitherto we have considered 
only appearances, and have not 
made the least inquiry as to the 
nature, magnitude, or distances of 
the celestial objects. 

Abstractly, there is no such thing 
as great and small, near and re- 
mote ; relatively speaking, however, 
we may apply the terms, great, and 
very great, as regards both mag- 
nitude and distance. Thus, an er- 
ror of ten feet in the measure of 
the length of a building, is very 
great — when an error of ten rods, 
in the measure of one hundred 
miles, would be too trifling to 
mention. 

Now if we consider the distance 
to the stars, it must be relative to 
some measure taken as a standard, 
or our inquiries will not be defi- 
nite, or even intelligible. We now 




Abstractly, is there any such thing as great and small ? When we use 
the terra great or small, does it imply a standard of measure ? Can the 
same amouni of error be both small and great at the same time. 



DISTANCES OF THE HEAVENLY BODIES. 69 

make this general inquiry : Are the heavenly bodies near to, or 
remote from, the earth? Here, the earth itself seems to be the 
natural standard for measure ; and if any body were but two, 
three, or even ten times the diameter of the earth, in distance, 
we should call it near; if 100, 200, or 2000 times the diameter 
of the earth, we should call it remote. To answer the inquiry, 
Are the heavenly bodies near or remote? we must put them to all 
possible mathematical tests ; a mere opinion is of no value, 
without the foundation of some positive knowledge. Let 1, 2, 
represent the absolute position of two stars ; and then, if A B 
C represents the circumference of the earth, these stars may 
be said to be near; but if a be represents the circumference 
of the earth, the stars are many times the diameter of the 
earth, in distance, and therefore may be said to be remote. If 
ABC is the circumference of the earth, in relation to these 
stars, the apparent distance of the two stars asunder, as seen 
from A, is measured by the angle 1 A 2 / and their apparent 
distance asunder, as seen from the point B, is measured by the 
angle 1 B 2; and when the circumference AB C is very large, 
as represented in our figure, the angle A, between the two 
stars, is manifestly greater than B. But if a b c is the circum- 
ference of the earth, the points a and b are relatively the same 
as A and B. And, it is an occular demonstration that the angle 
under which the two stars would appear at a is the same, or 
nearly the same, as that under which they would appear at b; 
or, at least, we can conceive the earth so small, in relation to 
the distance to the stars, that the angle under which two stars 
would appear, would be the same, seen from any point on the 
earth. 

Conversely, then, if the angle under which two stars appear 
is the same, as seen from all parts of the earth's surface, it is 
certain that the diameter of the earth is very small, compared 
with the distance to the stars; or, which is the same thing, 

To measure the distances to the heavenly bodies — what seems to be the 
natural standard of measure ? If the stars appeared at different distances 
asunder, as seen from different parts of the earth, what would that show V 



70 



ELEMENTARY ASTRONOMY 



the distance to the stars is many times the diameter of the earth. 
Therefore, observation has long since decided this important 
point. Sir John Herschel says : " The nicest measurements 
of the apparent angular distance of any two stars, inter se, 
taken in any parts of their diurnal course (after allowing for 
the unequal effects of refraction, or when taken at such times 
that this cause of distortion shall act equally on both), mani- 
fest not the slightest perceptible variation. Not only this, but 
at whatever point of the earth's surface the measurement is 
performed, the results are absolutely identical. No instruments 
ever yet invented by man are delicate enough to indicate, by 
an increase or diminution of the angle subtended, that one 
point of the earth is nearer to or farther from the stars than 
another." 

Perhaps the following view of this subject will be more 
intelligible to the general reader. 

Let Z H N 
H represent the 
celestial equator, 
as seen from the 
equator on the 
earth ; and if the 
earth be large, 
in relation to the 
distance to the 
stars, the obser- 
ver will be at z ; 
and the part of 
the celestial arc 
above his hori- 
zon would be represented by AZB, and the part below his ho- 
rizon by ANB, and these arcs are obviously unequal ; and 
their relation would be measured by the time a star or heav- 
enly body remains above the horizon, as seen from the equator, 

What is the testimony of Sir J. Herschel ? What do we infer from this 
fact ? What other illustration if given ? 




HORIZONTAL PARALLAX. 71 

compared with the time below it; but by observation, (refrac- 
tion being allowed for) not the least difference is to be discov- 
ered, and the stars are above the horizon as long as they are 
below ; which shows that the observer is not at z, but at z, 
and even more near the center ; so that the arc AZB, is imper- 
ceptibly unequal to the arc HNH; that is, they are equal to 
each other ; and the earth is comparatively but a point, in 
relation to the distance to the stars. 

This fact is well established, as applied to the fixed stars, 
sun and planets; but with the moon it is different : that body is 
longer below the horizon than above it, which shows that its 
distance from the earth is at least measurable. 

We view the moon from the earth, and it appears to cover a 
certain portion of the celestial circle, which we called the 
moon's apparent diameter; the half of this arc is called the semi- 
diameter. Now if we were at the moon to look down upon the 
earth, the semi-diameter of the earth would apparently cover a 
certain arc in the heavens, and this certain arc viewed from 
the moon is called the moon's 

HORIZONTAL PARALLAX. 

We place these two words into one line to make them con- 
spicuous, on account of their importance in astronomy. 

When we can find the horizontal parallax of any heavenly 
body, we can determine the distance of that body from the 
earth, as we shall soon explain. 

Parallax is the difference in position, of any body, as seen from 
the center of the earth, and seen from its surface. 

When a body is in the zenith of any observer, to him it has 
no parallax ; for he sees it in the same place in the heavens, as 
though he viewed it from the center of the earth. The great- 
est possible parallax that a body can have, takes place when 

As seen from the equator, do the stars remain as long above the horizon 
as below it ? What does that show ? Is the moon observed to be as long 
above the horizon, (after refraction is allowed for) as below it ? What 
does this fact show? What is parallax? When a body is in the zenith, 
has it any parallax ? Why ? 



72 



ELEMENTARY ASTRONOMY. 



the body is in the horizon of the observer ; and this parallax is 
called horizontal parallax. Hereafter, when we speak of the 
parallax of a body, horizontal parallax is to be understood, 
unless otherwise expressed. 

A clear and summary illustration of parallax in general, is 
given by the following figure: 

Let C be the 
center of the 
earth, Z the ob- 
server, and P, 
or p, the posi- 
tion of a body. 
From the cen- 
ter of the earth, 
the body is seen 
in the direction 
of the line CP, 
or Cp; from the 

observer at Z, it is seen in the direction of ZP, or Zp ; and 
the difference in direction, of these two lines, is parallax. When 
P is in the zenith, there is no parallax ; when P is in the 
horizon, the angle ZPC is then greatest, and it is the horizontal 
parallax. 

We now perceive that the horizontal parallax of any body is 
equal to the apparent semi-diameter of the earth, as seen from the 
body. The greater the distance to the body, the less is its 
horizontal parallax ; and when the distance is so great that the 
semi-diameter of the earth would appear only as a point, then 
the body has no parallax. Conversely, if we can detect no 
sensible parallax, we know that the body must be at a vast 
distance from the earth, and the earth itself must appear as a 
point from such a body, if, in fact, it were even visible. 

What is the position of a heavenly body when its parallax is greatest ? 
Why is parallax then called horizontal parallax ? When the distance of a 
body from the earth increases, does its horizontal parallax increase or 
decrease 1 




HORIZONTAL PARALLAX. 73 

Trigonometry gives the relation between the angles. and 
sides of every conceivable triangle ; therefore, we know all 
about the horizontal triangle ZCP, when we know CZ and 
the angles.* It is obvious that the less the angle ZPC the 
greater must be the distance CP ; that is, the less the hori- 
zontal parallax, the greater is the distance, and the difficulty, 
and the only difficulty, is to obtain the horizontal parallax, or 
the angle ZPC. 

The horizontal parallax cannot be directly observed, by 
reason of the great amount, and irregularity of horizontal 
refraction ; but if we can obtain a parallax at any considerable 
altitude, we can compute the horizontal parallax therefrom. 

The fixed stars have no sensible horizontal parallax, as we 
have frequently mentioned ; and the parallax of the sun is so 
small, that it cannot be directly observed; the moon is the 
only celestial body that comes forward and presents its paral- 
lax ; and from thence we know that the moon is the only body 
that is within a moderate distance of the earth. 

That the moon had a sensible parallax, was known to the 
earliest observers, even before mathematical instruments were 
at all refined ; but to decide upon its exact amount, and detect 

♦Calling the horizontal parallax of any body p, and the radius of the 
earth r, and the distance of the body from the center of the earth x, (the 
radius of the table always R, or unity), then, by trigonometry, we have, 

R : x : : sin.jt) : r. 
Therefore, 



\sin. PS 



From this equation we have the following general rule, to find the dis- 
tance to any celestial body : 

Rule. — Divide the radius of the tables by the sine of the horizontal parol- 
lax. Multiply that quotient by the se?ni-diameter of the earth, and the product 
will be the result. 

This result will, of course, be in the same terms of linear measure as the 
semi-diameter of the earth : that is, if r is in feet, the result will be in feet ; 
if r is in miles, the result will be in miles, etc. : 

Can horizontal parallax be directly observed ? Have the fixed stars any 
sensible parallax ? Why have they none ? Was the moon's parallax sen- 
sible to early observers ? 
7 



74 ELEMENTARY ASTRONOMY. 

its variations, required the combined knowledge and observa- 
tions of modern astronomers. 

The lunar parallax was first recognized in Europe, and in 
northern countries, by that luminary appearing to describe more 
than a semicircle south of the equator, and less than a simicircle 
north of thai line, during its revolutions among the stars, and, 
on an average, it was observed to be a longer time south, than 
north of the equator; but no suck inequality could be observed 
from the region of the equator. 

Observers at the south of the equator, observing the posi- 
tion of the moon, see it for a longer time north of the equator 
than south of it ; and, to them, it appears to describe more than a 
semicircle north of the equator. 

Here then, we have observation against observation, unless 
we can reconcile them. But the only reconciliation that can 
be made, is to conclude that the moon is really as long in one 
hemisphere as in the other, and the observed discrepancy must 
arise from the positions of the observers ; and when we reflect 
that parallax must always depress the object, and throw it 
farther from the observer, it is therefore perfectly clear that a 
northern observer should see the moon farther to the south 
than it really is, and a southern observer see the same body 
farther north than its true position. 

To find the amount of the lunar parallax requires the con- 
currence of two observers. They should be near the same 
meridian, and as far apart, in respect to latitude, as possible ; 
and every circumstance that could affect the result, must be 
known. 

The two most favorable stations are Greenwich (England) 
and the Cape of Good Hope. They would be more favorable 
if they were on the same meridian ; but the small change in 

By what observation was the moon's parallax shown ? Does the moon, 
on an average, appear to cross the equator to us, just at the time it really 
does cross the equator? Does parallax elevate or depress the object? 
How many observers are necessary to determine lunar parallax ? "What 
two stations are most favorable, aud why ? 



HORIZONTAL PARALLAX. 76 

declination, while the moon is passing from one meridian to 
the other, can be allowed for ; and thus the two observations 
are reduced to the same meridian, and are equivalent to being 
made at the same time. 

The most favorable times for such observations, are when 
the moon is near her greatest declinations, for then the change 
of declination is extremely slow. 

Let A represent the place of 
the Greenwich observatory, and 
B the station at the Cape of 
Good Hope. C is the center of 
the earth, and Z and Z' are the 
zenith points of the observers. 
Let j¥"be the position of the moon, 
and the observer at A will see it 
projected on the sky at m', and 
the observer at B will see it pro- 
jected on the sky at m. 

Now the figure ACBM is a 
quadrilateral ; the angle A CB is 
known by the latitudes of the two 
observers ; the angles MA C and 
MBC are the respective zenith 
distances, taken from 180°. 

But the sum of all the angles 
of any quadrilateral is equal to 
four right angles ; and hence the 
angles at A, C, and B, being 
known, the parallactic angle at M 
is known. 

In this quadrilateral, then, we 
have two sides, A C and CB, and all the angles ; and this is 
sufficient for the most ordinary mathematician to decide every 
particular in connection with it; that is, we can find AM, 3IB, 

What are most favorable times for observations ? Why ? In the figure 
before us, how is the angle M, determined ? 




76 ELEMENTAKY ASTBONOMY. 

and finally MC. Now MC being known, the horizontal paral- 
lax can be computed, for it is but a function* of the distance. 

The result of such observations, taken at different times, 
show all values to MC, between 55-jW, and 63 T 8 oV; taking the 
semi-diameter of the earth as unity. 

These variations are regular and systematic, both as to time 
and place, in the heavens ; and they show, without further in- 
vestigation, that the moon does not go round the earth in a 
circle, or, if it does, the earth is not in the center of that 
circle. 

The parallax corresponding to these extreme distances, are 
61' 29" and 53' 50". 

"When the moon moves round to that part of her orbit which 
is most remote from the earth, it is said to be in apogee; and, 
when nearest to the earth, it is said to be in perigee. The 
points apogee and perigee, mainly opposite to each other, do 
not keep the same place in the heavens, but gradually move 
forward in the same direction as the motion of the moon, and 
perform a revolution in a little less than nine years. 

Many times, when the moon comes round to its perigee, we 
find its parallax less than 61' 29", and, at the opposite apogee, 
greater than 53' 50". It is only when the sun is in, or near a 
line with the lunar perigee and apogee, that these greatest ex- 
tremes are observed to happen ; and when the sun is near a 
right angle to the perigee and apogee, then the moon moves 
round the earth in an orbit near a circle ; and thus, by observ- 
ing with care the variation of the moon's parallax, we find 
that its orbit is a revolving ellipse, of variable eccentricity. 

Because the moon's distance from the earth is variable, 

"Function of the distance, that is, horizontal parallax and distances are 
mathematically and invariably connected, as expressed in the following 
equation in which p is the parallax and x the distance MC. xs'm. p=r. 

How is it known that the moon's distance from the earth is visible ? 
What are the extreme distances ? "What is understood by apogee and by 
perigee? What is the figure of the lunar orbit? Is the orbit equally 
eccentric at all times ? When is the orbit nearest a circle ? 



HORIZONTAL PARALLAX. 77 

therefore there must be a mean distance : we shall show, here- 
after, that her motion is variable ; therefore there is a mean 
motion ; and as the eccentricity is variable, there is a mean 
eccentricity. 

The mean distance is 60.26, the semi-diameter of the earth, 
corresponding to the parallax of 57' 3". 

The variations in the moon's real distance must correspond to 
apparent variations in the moon's diameter ; and if the moon, or 
any other body, should have no variation in apparent diameter, 
we should then conclude that the body was always at the same 
distance from us. 

The change, in apparent diameter, of any heavenly body, is 
numerically proportional to its real change in distance. 

Now if the moon has a real change in distance, as observa- 
tions show, such change must be accompanied with apparent 
changes in the moon's diameter; and, by directing observa- 
tions to this particular, we find a perfect correspondence ; 
showing the harmony of truth, and the beauties of real 
science. 

We have several times mentioned that the moon's horizontal 
parallax is the semi-diameter of the earth, as seen from the 
moon ; which will be obvious by inspecting the following 
figure, in which E represents the semi-diameter of the earth, m 
the semi-diameter of the moon, and D the distance between 
them. The angle at the extremity E, takes in the moon's semi- 
diameter, and 
the like angle 
at the extrem- 
ity m is the 
moon's hori- 
zontal parallax, 
or the earth's semi-diameter, as seen from the moon. 

The variations of these two angles depend on the same cir- 
cumstance — the variation of the distance between the earth and 




What is the mean distance between the earth and the moon ? How is 
the change in the moon's distance indicated ? Does the moon's semi- 
diamoter and horizontal parallax correspond, in all their variations? 



78 ELEMENTARY ASTRONOMY. 

moon ; and, depending on one and the same cause, they must 
vary in just the same proportion. 

When the moon's horizontal parallax is greatest, the moon's 
semi-diameter is greatest; and, when least, the semi-diameter is 
the least ; and if we divide the tangent of the semi-diameter by 
the tangent of its horizontal parallax, we shall always find the 
same quotient (the decimal 0.27293); and that quotient is the 
ratio between the real diameter of the earth and the diameter 
of the moon. Having this ratio, and the diameter of the 
earth, 7912 miles, we can compute the diameter of the moon 
thus : 

7912X0.27293=2169.4 miles. 

As spheres are to each other in proportion to the cubes of 
their diameters, therefore the bulk (not mass) of the earth, is 
to that of the moon, as 1 to Jg-, nearly. 

It may be remarked, by every one, that we always see the 
same face of the moon ; which shows that she must roll on an 
axis, in the same time as her mean revolution about the earth ; 
for, if she kept her surface towards the same part of the 
heavens, it could not be constantly presented to the earth, 
because, to her view, the earth revolves round the moon, the 
same as to us the moon revolves round the earth ; and the 
earth presents phases to the moon, as the moon does to us, 
except opposite in time, because the two bodies are opposite In 
position. When we have new moon, the lunarians have full 
earth ; and when we have first quarter, they have last quarter, 
etc. The moon appears, to us, about half a degree in diam- 
eter ; the earth appears, to them, a moon, about two degrees in 
diameter, invariably fixed in their sky. 

The moon is an opake body, and shines only by reflecting 
the light of the sun, but its phases, its peculiar and variable 
path about the earth, and its periods of revolution, will be the 
subject of a future chapter. 

What is the ratio between the diameter of the earth and the diameter of 
the moon ? "What is the ratio between their masses, and how is it deter- 
mined ? What is the appearance of the earth as seen from the moon ? 



SOLAR PARALLAX, <fcc. 79 



CHAPTER II. 

SOLAR PARALLAX — DISTANCE TO THE SUN — CHANGES OF 
THE SEASONS — CLIMATE, &c. 

We have seen in the preceding chapter, that the horizontal 
parallax, and semi-diameter of any body, have a constant rela- 
tion to each other, and as we can distinctly observe the diame- 
ter of the sun, if we could observe his horizontal parallax we 
could then obtain the diameter of the sun, by the following 
proportion: 
H'shor. par. : ^semidia. : : diam. of earth : diam. of j|. 

But the sun's horizontal parallax is too small to be detected 
by any common means of observation ; hence it remained un- 
known, for a long series of years, although many ingenious 
methods were proposed to discover it. The only decision that 
ancient astronomers could make, concerning it, was, that it must 
be less than 20" or 15" of arc ; for, were it as much as that 
quantity, it could not escape observation. 

Now let us suppose that the sun's horizontal parallax is less 
than 20"; that is, the apparent semi-diameter of the earth, as 
seen from the sun, must be less than 20"; but the semi-diameter 
of the sun is 15' 56", or 956"; therefore the sun must be vastly 
larger than the earth — by at least 48 times its diameter; and 
the bulk of the earth must be, to that of the sun, in as high a 
ratio as 1 to the cube of 48. But as at present we do not 
suffer ourselves to know the true horizontal parallax of the 
sun, all the decision we can make on this subject is, that the 
sun is vastly larger than the earth. 

We shall now call to mind the fact, that the solar day is 
about 4 minutes longer than the sidereal day, which shows that 
the sun has an apparent motion eastward among the stars, 

By what proportion can we find the diameter of any heavenly body? 
Why can we not at present determine the diameter of the sun ? 



80 ELEMENTARY ASTRONOMY. 

and has the appearance of going round the earth once in a 
year : but the appearance would be the same, whether the earth 
revolves round the sun, or the sun round the earth, or both 
bodies revolve round a point between them. We are now to 
consider which is the most probable : that a large body should 
circulate round a much smaller one; or, the smaller one round a 
larger one. The last suggestion corresponds with our know- 
ledge and experience in mechanical philosophy ; the first is 
opposed to it. 

The apparent diameter of a heavenly body can be measured 
by the time it occupies in passing the meridian wire of a transit 
instrument, but for very small objects, such as the planets, the 
use of a micrometer is better. A micrometer is a pair of parallel 
wires near the focus of a telescope, which open and close by 
a mathematical contrivance, and the amount of opening is 
measured by the turns of a screw from the closing point, 
which amount determines the apparent diameter of the body. 

Observations can be made every clear day through the year, 
to determine the apparent diameter of the sun, and they have 
been made at many places, and for many years ; and the com- 
bined results show that the apparent diameter of the sun is 
the same, on the same day of the year, from whatever station 
observed. 

The least semi-diameter is 15' 45". 1 ; which corresponds, in 
time, to the first or second day of July ; and the greatest is 16' 
17".3, which takes place on the 1st or 2d of January. 

~Now as we cannot suppose that there is any real change in 
the diameter of the sun, we must impute this apparent change 
to real change in the distance of the body. 

Therefore the distance to the sun on the 30th of December, 

How do we know that the sun appears to move round the earth in a 
year ? Does the sun really move, or is it the earth that moves ? How can 
we measure the apparent diameter of a body ? What is a micrometer, 
give some general idea of one? Is the apparent diameter of the sun 
always the same? What must we infer from this fact? When is the 
apparent semi-diameter least ? When greatest ? Is the change uniform 
and gradual ? 



SOLAR PARALLAX, M. 81 

must be to its distance on the first day of July, as the number 
15' 45". 1 is to the number 16' 17".3, or as the number 945.1 to 
977.3 ; and all other days in the year, the proportional distance 
must be represented by intermediate numbers. 

From this, we perceive that the sun must go round the 
earth, or the earth round the sun, in very nearly a circle ; for 
were a representation of the curve drawn, corresponding to the 
apparent semi-diameter in different parts of the orbit, and 
placed before us, the eye could scarcely detect its departure 
from a circle. 

It should be observed, that the time elapsed between the 
greatest and least apparent diameter of the sun, or the reverse, 
is just half a year ; and the change in the sun's longitude is 
180°. 

If we consider the mean distance between the earth and 
sun as unity (as is customary with astronomers), and then 
put x to represent the least distance, and y the greatest dis- 
tance, we shall have 

x-\~y=2. 

And, - - x : y : : 9451 : 9773. 

A solution gives x=0. 98326, nearly, and y=1.01674, nearly; 
showing that the least, mean and greatest distance to the sun, 
must be very nearly as the numbers .98326, 1., and 1.01674. 

The fractional part, (.01674,) or the difference between the 
extremes and mean (when the mean is unity), is called the eccen- 
tricity of the orbit. 

In theory, the apparent diameters are sufficient to determine 
the eccentricity, could we really observe them to rigorous 
exactness ; but all luminous bodies are more or less affected 
by irradiation, which dilates a little their apparent diameters ; 
and the exact quantity of this dilatation is not yet well ascer- 
tained. 

How great is the elapsed time from one extreme to the other ? What is 
the difference in the sun's longitude ? "What is meant by the eccentricity 
of the earth's orbit? What is the amount of the eccentricity? 



82 ELEMENTARY ASTRONOMY. 

The eccentricity, as just mentioned, must not "be regarded as 
accurate. It is only a first approximation, deduced from the 
first and most simple view of the subject ; when we obtain full 
command over science, we can find methods which, with less 
care, will give more accurate results. 

The sun's right ascension and declination can be observed 
from any observatory, any clear day, and from thence we can 
trace its path along the celestial concave sphere above us, and 
determine, its change from day to day ; and we find it runs 
along a great circle called the ecliptic, which crosses the equa- 
tor at opposite points in the heavens ; and the ecliptic inclines 
to the equator with an angle of about 23° 27' 37". 

The plane of the ecliptic passes through the center of the 
earth, showing it to be a great circle, or what is the same 
thing, showing that the apparent motion of the sun has its 
center in the line which joins the earth and sun. 

The apparent motion of the sun along the ecliptic is called 
longitude ; and this is, its most regular motion. 

When we compare the sun's motion, in longitude, with its 
semi-diameter, we find a correspondence — at least, an apparent 
connection. 

When the semi-diameter is greatest, the motion in longitude 
is greatest; and, when the semi-diameter is least, the motion 
in longitude is least ; hit the two variations have riot the same 
ratio. 

When the sun is nearest to the earth, on or about the 30th 
of December, it changes its longitude, in a mean solar day, 
1° 1' 9". 95. When farthest from the earth, on the 1st of July, 
its change of longitude, in 24 hours, is only 57' 11 ".48. A 
uniform motion, for the whole year, is found to be 59' 8".33. 

The ancient philosophers contended that the sun moved 

What is understood by the ecliptic ? How can that circle be deter- 
mined ? What is the inclination of the ecliptic to the equator. What 
connection do we observe between the sun's semi-diameter, and its motion 
in longitude ? Do they both increase and decrease at the same time, and 
in the same ratio ? 



SOLAR PARALLAX, <fcc. 83 

about the earth in a circular orbit, and its real velocity uniform ; 
but the earth not being in the center of the circle, the same 
portion of the circle would appear under different angles ; and 
hence the variation in the sun's apparent angular motion. 

Now if this were a true view of the subject, the variation in 
the angular motion must be in exact proportion to the variation 
in distance ; that is, 945". 1 should be to 977".3 as 57' 11 ".48 to 
61' 9". 95, if the supposition of the first observers were true. 
But these numbers have not the same ratio ; therefore this sup- 
position was not satisfactory ; and it was probably abandoned 
for the want of this mathematical support. The ratio between 

945". 1 and 977".3 - 9773 = 1.0341, nearly; 

9451 J 

Between 57' 11 ".48 and 61' 9".95 3669 '-^=1.0694, nearly. 

3431".48 J 

If we square (1.0341) the first ratio, we shall have 1.06936, a 

number so near in value to the second ratio, that we conclude 

it ought to be the same, and would be the same, provided we 

had perfect accuracy in the observations. 

Thus we compare the angular motion of the sun in different 
parts of its orbit ; and we always find, that the inverse square of 
its distance is proportional to its angular motion ; and this incon- 
testible fact is so exact and so regular, that we lay it down as 
a law ; and if solitary observations do not correspond with it, 
we must condemn the observations, and not the law. 

By the aid of a little geometry in connection with this law,* 

* By making use of this law, we can find the eccentricity of the solar 
orbit, to greater precision than by the apparent diameters, because the same 
error of observation on longitude would not be as proportionally great as 
on apparent diameter. 

Let E be the eccentricity of the orbit ; then (1 — E) is the least distance to 
the sun, and (l-\-E) the greatest distance. Then, by observation, we have 

(1^-E) 2 : (\-\-E) 2 : : 57' 11".48 : 61'9".95; 
Or, (1— Ef : \\+E) 2 : : 343148 : 366995; 

Or, \—E : \-\-E : : ^343 148 : ^366995. 

Whence E=.0l67S8-f. 

What law exists between the distance of the sun and its angular motion ? 
What other law is derived from this one hy the aid of geometry ? 



84 



ELEMEE TARY ASTRONOMY. 



ic is easily demonstrated that the solar radius vector describes 
equal areas in equal times. This is one of Kepler's laws that 
applies to all the planets, and it is capable of an abstract geo- 
metrical demonstration. (See page 163, Univ. Ed.) 

If we draw lines from any point in a plane, reciprocally pro- 
portional to the sun's apparent diameter, and at angles differing 
as the change of the sun's longitude, and then connect the 
extremities of such lines made all round the point, the con- 
necting lines will form a curve, corresponding- with an ellipse, 
which represents the apparent solar orbit ; and, from a review 
of the whole subject, we give the following summary : 

1. The eccentricity of the solar ellipse, as determined from the 
apparent diameter of the sun, is .01674. 

2. The sun's angular velocity varies inversely as the square of 
its distance from the earth. 

3. The real velocity is inversely as the distance. 

4. The areas described by the radius vector are proportional to 
the times of description. 

We have several times mentioned, that, as far as appearances 
are concerned, it is immaterial whether we consider the sun 
moving round the earth, or the earth round the sun ; for, if the 

earth is in one position 
of the heavens, the sun 
will appear exactly 
in the opposite position, 
and every motion made 
by the earth must cor- 
respond to an apparent 
motion made by the sun. 
But for the purpose 
of being nearer to fact, 
we will now suppose that the earth revolves round the sun in an 
elliptical orbit, as represented in the figure in the margin. 

What figure will represent the solar orbit? Would appearances be the 
same, whether the earth moved round the sun, or the sun round the earth ? 




SOLAR PARALLAX, <fcc. 85 

We have very much exaggerated the eccentricity of the 
orbit, for the purpose of bringing principles clearer to view. 

The greatest and least distances, from the sun to the earth, 
make a straight line through the sun, and cut the orbit into two 
equal parts. 

When the earth is at B, the sun is said to be in apogee, or 
the earth is said to be in its aphelion ; when the earth is at A, 
the sun is said to be in perigee, or the earth is said to be in its 
perihelion, 

The line joining these two points is the major diameter of the 
orbit ; and it is the only diameter passing through the sun, that 
cuts the orbit into two equal parts. 

Now, as equal areas are described in equal times, it follows 
that the sun must be just half a year in passing from apogee 
to perigee, and from perigee to apogee ; provided that these 
points are stationary in the heavens, and they are so, very 
nearly. 

If we suppose the earth moves along the orbit from D to A, 
and Ave observe the sun from D, and continue observations 
upon it until the earth comes to C, then the longitude of the 
sun has changed 180° ; and if the time is less than half a year, 
we are sure the perigee is in this part of the orbit. If we con- 
tinue observations round and round, and find where 180° of 
longitude correspond with half a year, there will be the posi- 
tion of the longer axis ; which is sometimes called the line of 
the apsides. 

By this method the position of the longer axis is more accu- 
rately ascertained than it could be by observing variations in 
the sun's apparent diameter, because the variations of apparent 
diameter are quite imperceptible, for several degrees, at the 
extremities of the major axis. 

The longitude of the aphelion, for the year 1801, was 99° 
51' 9", and of course, the perihelion was in longitude 279° 

What line, passing through the sun, will cut the orbit of the earth into 
two equal parts? Does the sun describe 180° from any point in just half 
a year, or must it be from some particular point? How do astronomers 
rind the position of the major axis? What was the portion of it in 1801? 



86 ELEMENTARY ASTRONOMY. 

51' 9". These points move forward, in respect to the stars, 
about 12" annually, and, in respect to the equinox, about 62"; 
more exactly 61 ".905, and, of course, this is their annual in- 
crease of longitude. 

In the year 1250, the perigee of the sun coincided with the 
winter solstice, and the apogee with the summer solstice ; and 
at that time the sun was 178 days and about 17-i- hours on the 
south side of the equator, and 186 days and about 12-J- hours 
on the north side ; being longer in the northern hemisphere 
than in the southern, by seven days and 19 hours. At present, 
the excess is seven days and near 17 hours. 

As the sun is a longer time in the northern than in the south- 
ern hemisphere, the first impression might be, that more solar 
heat is received in one hemisphere than in the other; but the 
amount is the same ; for whatever is gained in time, is lost in 
distance ; and what is lost in time, is gained by a decrease of 
distance. The amount of heat depends on the intensity multi- 
plied by the time it is applied ; and the product of the time 
and distance to the sun, is the same in either hemisphere ; but 
the amount of heat received, for a single day, is different in 
the two hemispheres. 

When the earth is at B and at A, the mean and true longi- 
tude, of the sun agree ; at all other points the mean place of 
the sun is not the same as its true place. The mean place can 
be determined by the time from the apogee or perigee points, 
and the true place can be determined by meridian observations 
at any observatory. The difference between these two places 
is noted and put down in a table called the equation of the sun's 
center. The equation of the center can also be determined by 
mathematical computation when once the eccentricity of the 
ellipse is known. 

Are there different degrees of heat received in the different hemispheres 
during the year ? What does the amount of heat depend upon ? What is 
meant by the equation of the sun's center ? 



THE CAUSES OF THE CHANGE OF SEASONS. 



87 



CHAPTER III 



THE CAUSES OF THE CHANGE OF SEASONS. 



The annual revolution of the earth in its orbit, combined 
with the position of the earth's axis to the plane of its orbit, 
produces the change of the seasons. 

If the axis were perpendicular to the plane of its orbit, there 
would be no change of seasons, and the sun would then be all 
the while in the celestial equator. 

This will be understood by the following figure. Conceive 
the plane of the paper to be the plane of the earth's orbit, and 
conceive the several representations of the earth's axis, JVS, 
to be inclined to the paper at an angle of 66° 32'. 




In all representations of JYS, one half of it is supposed to 
be above the paper, the other half below it. 

]\ r S is always parallel to itself; that is, it is always in the 

What produces the change of seasons ? 



88 ELEMENTARY ASTRONOMY. 

same position — always at the same inclination to the plane of 
its orbit — always directed to the same point in the heavens, 
in whatever part of the orbit the earth may be. 

The plane of the equator represented by Eq, is inclined to 
the plane of the orbit by an angle of 23° 28'. 

By inspecting the figure, the reader will gather a clearer 
view of the subject than by whole pages of description : he 
will perceive the reason why the sun must shine over the north 
pole, in one part of its orbit, and fall as far short of that point 
when in the opposite part of its orbit ; and the number of de- 
grees of this variation depends, of course, on the position of 
the axis to the plane of the orbit. 

Now conceive the line XS to stand perpendicular to the 
plane of the paper, and continue so ; then Eq would lie on the 
paper, and the sun would at all times be in the plane of the 
equator, and there would be no change of seasons. If XS 
were more inclined from the perpendicular than it now is, then 
we should have a greater change of seasons. 

By inspecting the figure, we perceive, also, that when it is 
summer in the northern hemisphere, it is winter in the southern; 
and conversely, when it is winter in the northern, it is summer 
in the southern. 

When a line from the sun makes a right angle with the 
earth's axis, as it must do in two opposite points of its orbit, 
the sun will shine equally on both poles, and it is then in the 
plane of the equator ; which gives equal days and nights the 
world over. 

Equal days and nights, for all places, happen on the 20th of 
March of each year, and on the 22d or 23d of September. At 
these times the sun crosses the celestial equator, and it is said 
to be in the equinox. 

The longitude of the sun at the vernal equinox, is 0° ; and 
at the autumnal equinox, its longitude is 180°. 

What is the inclination of the earth's axis to the plane of its orbit ? If 
the inclination were 90°, would there be any change of seasons ? Does the 
earth 's axis yl^avs keep the same position ? How do we know that ? 



THE CAUSES OF THE CHANGE OF SEASONS. 83 

The time of the greatest north declination is the 20th of 
June ; the sun's longitude is then 90°, and is said to be at the 
summer solstice. 

The time of the greatest south declination is the 22d of 
December ; the sun's longitude, at that time, is 270°, and is 
said to be at the winter solstice. 

By inspecting the figure, we perceive, that when the earth 
is at the summer solstice, the north pole, P, and a considera- 
ble portion of the earth's surface around, is within the enlight- 
ened half of the earth ; and as the earth revolves on its axis 
ITS, this portion constantly remains enlightened, giving a con- 
stant day — or a day of weeks and months duration, according 
as any particular point is nearer, or more remote from the pole : 
the pole itself is enlightened full six months in the year, and 
the circle of more than 24 hours constant sunlight, extends to 
23° 28' from the pole (not estimating the effects of refraction). 
On the other hand, the opposite, or south pole, S, is in a long 
season of darkness, from which it can be relieved only by the 
earth changing position in its orbit. 

"Now, the temperature of any part of the earth's surface 
depends mainly, if not entirely, on its exposure to the sun's 
rays. Whenever the sun is above the horizon of any place, 
that place is receiving heat ; when below, parting with it, by 
the process called radiation ; and the whole quantities received 
and parted with in the year, must balance each other at every 
station, or the equilibrium of temperature would not be sup- 
ported. Whenever, then, the sun remains more than 12 hours 
above the horizon of any place, and less beneath, the general 
temperature of that place will be above the average ; when the 
reverse, below. As the earth, then, moves from A to B, the 
days growing longer, and the nights shorter, in the northern 
hemisphere, the temperature of every part of that hemisphere 

"When does the sun attain its greatest northern declination? When its 
greatest southern declination? Is there any night at the north pole while 
the sun's declination is north ? What is the extent of constant daylight 
from the pole when the sun's declination is 18 degrees north? 
8 



90 ELEMENTARY ASTRONOMY. 

increases, as we pass from spring to summer, while at the same 
time the reverse is going on in the southern hemisphere. As 
the earth passes from B to C, the days and nights again ap- 
proach to equality — the excess of temperature in the northern 
hemisphere, above the mean state, grows less, as well as its 
defect in the southern ; and at the autumnal equinox, C, the 
mean state, is once more attained. From thence to D, and, 
finally round again to A, all the same phenomena, it is obvious, 
must again occur, but reversed; it being now winter in the 
northern, and summer in the southern, hemisphere." 

The inquiry is sometimes made, why we do not have the 
warmest weather about the summer solstice, and the coldest 
weather about the winter solstice. 

This would be the case if the sun immediately ceased to 
give extra warmth, on arriving at the summer solstice ; but if 
it could radiate extra heat to warm the earth three weeks before 
it came to the solstice, it would give the same extra heat three 
weeks after ; and the northern portion of the earth must con- 
tinue to increase in temperature as long as the sun continues 
to radiate more than its medium degree of heat over the sur- 
face, at any particular place. Conversely, the whole region of 
country continues to grow cold as long as the sun radiates less 
than its mean annual degree 01 heat over that region. The 
medium degree of heat, for the whole year, and for all places, 
of course, takes place when the sun is on the equator ; the 
average temperature, at the time of the two equinoxes. The 
medium degree of heat, for our northern summer, considering 
only two seasons in the year, takes place when the sun's decli- 
nation is about 12 degrees north ; and the medium degree of 
heat, for winter, takes place when the sun's declination is about 
1 -2 degrees south ; and if this be true, the heat of summer will 
becrin to decrease about the 20th of August, and the cold of 

Why is not the 20th of June considered as mid-summer in the 
northern hemisphere, — or, rather, why is July the mid-summer season, 
and not June ? A: what time may we expect the severity of winter to 
he pa=: ! 



THE CAUSES OF THE CHANGE OF SEASONS. 91 

winter must essentially abate, on, or about the 16th of Febru- 
ary^ in all northern latitudes. 

The warmest part of the day, (other circumstances being 
equal,) is not at 12, but about 2 o'clock in the afternoon. The 
sun is then west of the meridian, and its rays will strike more 
perpendicularly on a plane whose downward slope is towards 
the west, than on one, whose downward slope is towards the 
east. 

This will account for the fact, that climates are more mild 
west of mountain ranges than on the eastern side of the same 
mountains, other circumstances being equal. The vicinity of 
large bodies of water, and the general elevation of the country 
above the level of the sea, have much to do with climate, but 
as these causes have no particular connection with astronomy, 
we omit them. 

What time of day is warmest ? Why not at noon ? Which locality has 
the warmest climate, on the east or west side of the Alleghany mountains, 
in the same latitude and at the same elevation above the sea ? 



92 ELEMENTARY ASTRONOMY. 

CHAPTER IV. 
EQUATION OF TIME. 

Wje now come to one of the most important subjects in 
astronomy — the equation of time. 

Without a good knowledge of this subject, there will be 
constant confusion in the minds of the pupils ; and such is the 
mature of the case, that it is difficult to understand even the 
facts, without investigating their causes. 

Sidereal time has no equation ; it is uniform, and, of itself, 
oerfect and complete. 

The time, by a perfect clock, is theoretically perfect and 
complete, and it is called mean solar time. 

The time, by the sun, is not uniform ; and, to make it agree 
with the perfect clock, requires a correction — a quantity to 
make equality ; and this quantity is called the equation of 
time.* 

If the sun were stationary in the heavens, like a star, it 
i^ould come to the meridian after exact and equal intervals 
<^f time ; and, in that case, there would be no equation of 
time. 

If the sun's motion, in right ascension, were uniform, then 
it would also come to the meridian after equal intervals of 
time, and there would still be no equation of time. But 
(speaking in relation to appearances) the sun is not stationary 
in the heavens, nor does it muve uniformly ; therefore it can- 
not come to the meridian at equal intervals of time, and, of 
course, the solar days must be slightly unequal. 

* In astronomy, the term equation, is applied to all corrections, to con- 
vert a mean to its true quantity. 

Are all sidereal days alike in length? Are all solar days alike in 
length ? If solar days are unequal in length, what will it produce? 



EQUATION OF TIME. 93 

When the sun is on the meridian, it is then apparent noon 
for that day : it is the real solar noon, or, the half elapsed time 
between sunrise and sunset. 

A fixed star comes to the meridian at the expiration of every 
23h. 56m. 04.09s. of mean solar time ; and if the sun were 
stationary in the heavens, it would come to the meridian after 
every expiration of just that same interval. But the sun in- 
creases its right ascension every day, by its apparent eastward 
motion ; and this increases the time of its coming to the meri- 
dian; and the mean interval between its successive transits 
over the meridian is just 24 hours ; but the actual intervals 
are variable — some less, and some more, than 24 hours. 

On and about the 1st of April, the time from one meridian 
of the sun to another, as measured by a perfect clock, is 23h. 
59m. 52.4s. ; less than 24 hours by about 8 seconds. Here, 
then, the sun and clock must be constantly separating. On 
and about the 20th of December, the time from one meridian 
of the sun to another is 24h. 0m. 24.2s., more than 24 seconds 
over 24 hours ; and the daily accumulation of a few seconds 
will soon amount to minutes — and thus the sun and clock will 
become very sensibly separated — and this is the equation of 
time. 

To detect the law which separates the sun and clock, and 
find the amount of separation for any particular day, we must 
consider 

1st. The unequal apparent motion of the sun along the ecliptic. 

2d. The variable inclination of this motion to the equator. 

If the sun's apparent motion along the ecliptic were uniform, 
still there would be an equation of time ; for that motion, in 
some parts of the orbit, is oblique to the equator, and, in other 
parts, parallel with it ; and its eastward motion, in right ascen- 
sion, would be greatest when moving parallel with the equator. 

"When is it apparent noon? "When is it mean noon? The differenc-e 
between these two noon's is always equal to what ? I| the sun's apparent 
motion along the ecliptic were uniform, would there still be an equation 
of time, and why ? 



94 ELEMENTARY ASTRONOMY. 

From the first cause, separately considered, the sun and 
clock would agree two days in a year — the 1st of July and the 
30th of December. 

From the second cause, separately considered, the sun and 
clock agree four days in a year — the days when the sun 
crosses the equator, and the days he reaches the solsticial 
points. 

When the results of these two causes are combined, the sun 
and clock will agree four days in the year ; but it is on neither 
of those days marked out by the separate causes ; and the 
intervals between the several periods, and the amount of the 
equation, appear to want regularity and symmetry. 

The four days in the year on which the sun and clock agree, 
that is, show noon at the same instant, are April 15th, June 
16th, September 1st, and December 24th. 

The elliptical form of the earth's orbit gives rise to the une- 
qual motion of the earth in its orbit, and thence to the appa- 
rent unequal motion of the sun in the ecliptic ; and this same 
unequal motion is what we have denominated the first cause of 
the equation of time. Indeed, this part of the equation of 
time is nothing more than the equation of the sun's center, 
changed into time, at the rate of four minutes to a degree. 

The greatest equation for the sun's longitude, is by obser- 
vation 1° 55' 30"; and this, proportioned into time, gives 7m. 
42s. for the maximum effect in the equation of time arising 
from the sun's unequal motion. When the sun departs from 
its perigee, its motion is greater than the mean rate, and, of 
course, comes to the meridian later than it otherwise would. 
In such cases, the sun is said to be slow — and it is slow all 
the way from its perigee to its apogee ; and fast in the other 
half of its orbit. 

On what days in the year would the sun and clock agree, if the sun's 
motion were uniform along the ecliptic ? On what days in the year do 
the sun and clock agree ? What is the maximum effect for the sun's une- 
qual motion ? 




EQUATION OF TIME. 95 

For a more particular explanation of the second cause, we 
must call attention to the figure in the margin. 

Let °p @ loj represent the ecliptic, and °p lhj the 
equator. 

By the first correc- 
tion, the apparent mo- 
tion along the ecliptic is 
rendered uniform ; and 
the sun is then supposed 
to pass over equal spaces 
in equal intervals of 
time along the arc n p S 
@. But equal spaces 
of arc, on the ecliptic, 
do not include the same 
meridians, as equal spa- 
ces on the equator. In 
short, the points on the 

ecliptic must be reduced to corresponding points on the equator. 
For instance, the number of degrees represented by C] f' S on the 
ecliptic, is greater than to the same meridian along the equator. 
The difference between 'f' S and r p S', turned into time, is the 
equation of time arising from the obliquity of the ecliptic cor- 
responding to the point S. 

At the points r p, @, and lqj, and also at the southern tropic, 
the ecliptic and the equator correspond to the same meridian ; 
but all other equal distances, on the ecliptic and equator, are 
included by different meridians. 

It will be observed, by inspecting the figure, that what the 
sun loses in eastward motion, by oblique direction near the equa- 
tor, is made up, when near the tropics, by the diminished dis- 
tances between the meridians. 

For a more definite understanding of this matter, we ffive 
the following table : 

When does the sun lose most in eastward motion on the ecliptic ? 
When does it gain most in eastward motion ? 



96 



LLEUES T ARY ASTRONOMY 



Table showing the separate results of the two causes for the equa- 
tion of time, corresponding to every fifth day of the second years 
after leap year ; but is nearly correct for any year. 







1st cause. 


2d cause. 




1st cause 


2d cause. 






Sun slow 


Sun slow 




Si'n fast. 


Sun fast. 






of Clock. 


of Clock. 












m. s. 


m. s. 




m. s. 


m. s. 


January 


5 


41 


5 8 


July 1 





3 32 




10 


1 22 


6 35 


7 


40 


5 8 




15 


2 2 


7 48 


12 


1 19 


6 35 




20 


2 41 


8 45 


17 


1 57 


7 48 




25 


3 19 


9 26 


22 


2 35 


8 45 




29 


3 56 


9 49 


28 


3 12 


9 26 


February 3 


4 30 


9 53 


August 2 


3 47 


9 49 




8 


5 2 


9 40 


7 


4 21 


9 53 




13 


5 32 


9 9 


12 


4 52 


9 40 




18 


5 39 


8 23 


17 


5 22 


9 9 




23 


6 24 


7 22 


22 


5 50 


8 23 




28 


6 45 


6 9 


28 


6 14 


7 22 


March 


5 


7 3 


4 46 


Sept. 2 


6 36 


6 9 




10 


7 18 


3 15 


7 


6 56 


4 46 




15 


7 29 


1 39 


12 


7 12 


3 15 




20 


7 37 


sun fast. 


17 


7 24 


1 39 




25 


7 42 


1 39 


23 


7 34 


sun fast. 




30 


7 42 


3 15 


28 


7 40 


1 39 


April 


4 


7 40 


4 46 


October ' 3 


7 42 


3 15 




9 


7 34 


6 9 


8 


7 40 


4 46 




14 


7 24 


7 22 


13 


7 34 


6 9 




19 


7 12 


8 23 


18 


7 24 


7 22 




24 


6 56 


9 9 


23 


7 12 


8 23 




30 


6 36 


9 40 


28 


6 56 


9 9 


May 


5 


6 14 


9 53 


Not. 2 


6 36 


9 40 




10 


5 50 


9 49 


7 


6 14 


9 53 




15 


5 22 


9 26 


12 


5 50 


9 49 




20 


4 52 


8 45 


17 


5 22 


9 26 




26 


4 21 


7 48 


22 


4 52 


8 45 




31 


3 47 


6 35 


27 


4 22 


7 48 


June 


5 


3 12 


5 8 


Dec. 2 


3 47 


6 35 




10 


2 35 


3 32 


7 


3 12 


5 8 




16 


1 57 


1 48 


12 


2 35 


3 32 




21 


1 19 


sun slow 


17 


1 57 


1 48 




26 


40 


1 48 


21 

26 


1 19 

40 


sun slow 
1 48 



By this table, the regular and symmetrical result of each 
cause is visible to the eye ; but the actual value of the equa- 
tion of time, for any particular day. is the combined results 



What is the first cause of the equation of time ? What is the second 
cause ? 



EQUATION OF TIME. 97 

of these two causes. Thus, to find the equation of time for 
the 5th day of March, we look in the table and find that 

The first cause gives sun slow - - 7m. 3s. 

The second " sun slow - 4 46 



Their combined result (or algebraic sum) is 11 49 slow. 

That is, the sun being slow, it does not come to the meridian 
until 11m. 49s. after the noon shown by a perfect clock ; but 
whenever the sun is on the meridian, it is then noon, apparent 
time ; and, to convert this into mean time, or to set the clock, 
we must add 11m. 49s. 

By inspecting the table, we perceive that on the 14th of 
April the two results nearly counteract each other ; and conse- 
quently the sun and clock nearly agree, and indicate noon at 
the same instant. On the 2d of November the two results 
unite in making the smi fast; and the equation of time is then 
the sum of 6 36 and 9 40, or 16m. 16s. ; the maximum result. 

The sun at this time being fast, shows that it comes to the 
meridian 16m. 16s. before 12 o'clock, true mean time; or, 
when the sun is on the meridian, the clock ought to show llh. 
43m. 44s. ; and thus, generally, when the sun is fast, we must 
subtract the equation of time from apparent time, to obtain mean 
time; and add, when the sun is slow. 

As no clock can be relied upon, to run to true mean time, 
or to any exact definite rate, therefore clocks must be frequently 
rectified by the sun. "We can observe the apparent time, and 
then, by the application of the equation of time, we determine 
the true mean time. 

A table for the equation of time, corresponding to each 
degree of the sun's longitude, is to be found in many astro- 
nomical works, and such a table would be perpetual, provided 
the longer axis of the solar orbit did not change its position in 
relation to the equinox. But as that change is very sloiv, a 

When is the sun said to be slow ? When fast ? Can any clock be relied 
upon to run to mean time ? How then is mean time discovered ? Vi hy can 
Tveiiot hare a perpetual table for the equation of time? 




98 ELEMENTARY ASTRONOMY. 

table of that kind will serve for many years, with a trifling 
correction. 

We repeat, sidereal time is the interval of time elapsed since 
the equinoctial point in the heavens passed the meridian. 

The solar day is 3m. 56s. 55 of sidereal time, longer than a 
sidereal day. 

At the instant of mean noon, Greenwich time, on the 1st of 

March, 1857, the sidereal time was 

h. m. 8. 
Estimated at - - - - 22 36 56.65 

To this add 3 56.55 



Sidereal time at noon, March 2d, 22 40 53.20 

Thus we might compute the sidereal time at mean noon, 
Greenwich time, for any number of days, (omitting 24h. when 
we passed that sum.) 

At mean noon, the right ascension of the sun, plus or minus 
the equation of time, is always equal to the sidereal time. 

Twenty-four hours of mean solar time is equal to 24h. 3m. 
56s. 55 of sidereal time. Therefore eight hours of solar time is 
equal to 8h. lm. 18s. 82 of sidereal time ; and thus we may 
correct any hour of solar time to its corresponding value of 
sidereal time. 

On the 1st day of May, 1857, at mean noon, 

h. m. s. 

The sidereal time was - - - 2 37 26.46 

Add, 8 1 18.82 



Sidereal time at 8, mean time, - 10 38 45.28 
Thus we might find the sidereal time corresponding to any 

other hour, on any other day, having the use of a Nautical 

Almanac. 

It is very important that the navigator, astronomer, and clock 

regulator, should thoroughly understand the equation of time ; 

and persons thus occupied pay great attention to it ; but most 

people in common life are hardly aware of its existence. 

To whom is equation of time important ? 



APPARENT MOTIONS OF THE PLANETS. 09 

CHAPTER V. 
THE APPARENT MOTIONS OF THE PLANETS. 

We have often reminded the reader of the great regularity 
of the fixed stars, and of their uniform positions in relation to 
each other ; and by this very regularity and constancy of rela- 
tive positions, we denominate them fixed; but there are certain 
other celestial bodies, that manifestly change their positions 
in space, and, among them, the sun and moon are most prom- 
inent. 

In previous chapters, we have examined some facts con- 
cerning the sun and moon, which we briefly recapitulate, as 
follows : 

1. That the sun's distance from the earth is very great; but 
at present we cannot determine how great, for the want of one 
element — its horizontal parallax. 

2. Its magnitude is much greater than that of the earth. 

3. The distance between the sun and earth is slightly varia- 
ble ; but it is regular in its variations, both in distance and in 
apparent angular motion. 

4. The moon is comparatively very near the earth ; its 
distance is variable, and its mean distance and amount of 
variations are known. It is smaller than the earth, although, 
to the mere vision, it appears as large as the sun. 

The apparent motions of both sun and moon are always in 
one direction ; and the variations of their motions are never 
far above or below the mean. 

But there are several other bodies that are not fixed stars ; 
and although not as conspicuous as the sun and moon, have 
been known from time immemorial. 

What is repeated in chapter v. concerning the fixed stars ? What is 
mentioned again concerning the &un ? What iu relation to the moon ? 



100 ELEMENTARY ASTRONOMY. 

They appear to belong to one family ; but, before the true 
system of the world was discovered, it was impossible to give 
any rational theory concerning their motions, so irregular and 
erratic did they appear ; and this very irregularity of their 
apparent motions induced us to delay our investigations con- 
cerning them to the present chapter. 

In general terms, these bodies are called planets — and there 
are several of recent discovery — and some of very recent 
discovery ; but as these are not conspicuous, nor well known, 
all our investigations of principles will refer to the larger 
planets, Venus, Mars, Jupiter, and Saturn. We now com- 
mence giving some observed facts, as extracted from the Cam- 
bridge astronomy. 

" There are few who have not observed a beautiful star in 
the west, a little after sunset, and called, for this reason, the 
evening star. This star is Venus. If we observe it for several 
days, we find that it does not remain constantly at the same 
distance from the sun. It departs to a certain distance, which 
is about 45°, or -*th of the celestial hemisphere, after which it 
begins to return ; and as we can ordinarily discern it with the 
naked eye only when the sun is below the horizon, it is visible 
only for a certain time immediately after sunset. Subsequently 
it sets with the sun, and then we are entirely prevented from 
seeing it by the sun's light. But after a few days, we perceive 
in the morning, near the eastern horizon, a bright star which 
was not visible before. It is seen at first only a few minutes 
before sunrise, and is hence called the morning star. It departs 
from the sun from day to day, and precedes its rising more and 
more ; but after departing to about 45°, it begins to return, 
and rises later each day ; at length it rises with the sun, and 
we cease to distinguish it. In a few days the evening star 
again appears in the west, very near the sun ; from which it 
departs in the same manner as before ; again returns ; disap- 

What bodies are planets ? In what respects do their motions diflFer from 
the fixed stars? Why has the author delayed mentioning these bodies 
until now ? What planet is called the morning and evening star ? 



APPARENT MOTIONS OF THE PLANETS. 101 

pears for a short time ; and then, the morning star presents 
itself. 

These alternations, observed without interruption for more 
than 2000 years, evidently indicate that the evening and morn- 
ing star are one and the same body. They indicate, also, that 
this star has a proper motion, in virtue of which it oscillates 
about the sun, sometimes preceding and sometimes following it. 

These are the phenomena exhibited to the naked eye ; but 
the admirable invention of the telescope enables us to carry 
our observations much farther." 

On observing Venus with a telescope, the irradiation is, in a 
great measure, taken away, and we perceive that it has phases, 
like the moon. At evening, when approaching the sun, it pre- 
sents a luminous crescent, the points of which are from the 
sun. The crescent diminishes as the planet draws nearer the 
sun ; but after it has passed the sun, and appears on the other 
side, the crescent is turned in the other direction ; the enlight- 
ened part always toward the sun, showing that it receives its 
light from that great luminary. The crescent now gradually 
increases to a semicircle, and finally, to a full circle, as the 
planet again approaches the sun ; but, as the crescent increases, 
the apparent diameter of the planet diminishes; and at every 
alternate approach of the planet to the sun, the phase of the 
planet is full, and the apparent diameter small ; and at the 
other approaches to the sun, the crescent diminishes down to 
zero, and the apparent diameter increases to its maximum. 
When very near the sun, however, the planet is lost in the 
sunlight ; but at some of these intervals, between disappearing 
in the evening and reappearing in the morning, it appears to 
run over the sun's disc as a round, black spot ; giving a fine 
opportunity to measure its greatest apparent diameter. When 
Venus appears full, its apparent diameter is not more than 10", 
and when a black spot on the sun, it is 59".8, or very nearly 1\ 

How do we know that the morning and evening star must be the same 
body ? What is the appearance of the planet when viewed through a tel- 
escope ? How does it appear that Venus receives its light from the sun ? 



102 ELEMENTARY ASTRONOMY. 

Hence, its greatest distance must be, to its least distance, a3 
59". 8 to 10, or nearly as 6 to 1. 

The learner should impress this fact on his mind, that this 
planet is always in the same part of the heavens as the sun — 
never departing more than 47° on each side of it — called its 
greatest elongation. In consequence of being always in th6 
neighborhood of the sun, it can never come to the meridian 
near midnight. Indeed, it always comes to the meridian within 
three hours twenty minutes of the sun, and, of course, in day- 
light. But this does not prevent meridian observations being 
taken upon it, through a good telescope ;* and, as to this par- 
ticular planet, it is sometimes so bright as to be seen by the 
unassisted eye in the daytime. 

Even without instruments and meridian observations, the 
attentive observer can determine that the motion of Venus, in 
relation to the stars, is very irregular — sometimes its motion 
is very rapid — sometimes slow — - sometimes direct — some- 
times stationary, and sometimes retrograde ;\ but the direct 
motion prevails, and, as an attendant to the sun, and in its own 
irregular manner, as just described, it appears to traverse round 
and round among the stars. 

But Venus is not the only planet that exhibits the appear- 
ances we have just described. There is one other, and only 
one — Mercury; a very small planet, rarely visible to the naked 

* The stars continue visible through telescopes, during the day, as well 
as the night ; and that, in proportion to the power of the instrument, not 
only the largest and brightest of them, but even those of inferior luster, 
such as scarcely strike the eye, at night, as at all conspicuous, are readily 
found and followed, even at noonday, by those who possess the means of 
pointing a telescope accurately to the proper places — unless the star is in 
that point of the heavens very near the sun. — Herschel. 

f In astronomy, direct motion is eastward among the stars ; stationary is 
no apparent motion ; and retrograde is a westward motion. 

Is the distance of Venus from the earth very variable, and how great is 
the variation? How is that fact ascertained ? Describe the apparent 
motion of Venus among the stars. What is understood by stationary, 
in astronomy? "What by direct and retrograde motions? What other 
planet exhibits like appearances to Venus ? 



APPARENT MOTIONS OF THE PLANETS. 103 

eye, and not known to the very ancient astronomers. "Vv hat- 
ever description we have given of Venus applies to Mercury, 
except in degree. Its variations of apparent diameter are not 
so great, and it never departs so far from the sun ; and the 
interval of time, between its vibrations from one side to the 
other of the sun, is much less than that of Venus. 

These appearances clearly indicate that the sun must be the center, 
or near the center, of these motions, and not the earth ; and that 
Mercury must revolve in. an orbit within that of Venus. 

So clear and so unavoidable were these inferences, that even 
the ancients (who were the most determined advocates for the 
immobility of the earth, and for considering it as the principal 
object in creation — the center of all motion, etc.) were com- 
pelled to admit them ; but with this admission, they contended, 
that the sun moved round the earth, carrying these planets as 
attendants. 

By taking observations on the other planets, the ancient 
astronomers found them variable in their apparent diameters, 
and angular motions ; so much so, that it was impossible to recon- 
cile appearances with the idea of a stationary point of observation; 
unless the appearances were taken for realities, and that was 
against all true notions of philosophy. 

The planet Mars is most remarkable for its variations ; and 
the great distinction between this planet and Venus, is, that it 
does not always accompany the sun ; but it sometimes, yea, at 
regular periods, is in the opposite part of the heavens from the 
sun — called Opposition — at which time it rises about sunset, 
and comes to the meridian about midnight. 

The greatest apparent diameter of Mars takes place when 
the planet is in opposition to the sun, and it is then 1 7". 1 ; and 
its least apparent diameter takes place when in the neighbor- 

What do these appearances clearly indicate ? What is the planet Mars 
most remarkable for ? What great distinction is there between some ap- 
pearances of Mars and Yenus ? When a planet is in opposition to the sun, 
what time of the day does it pass the meridian ? What is shown by the 
great variation in the apparent diameter of Mars ? 



104 ELEMENTARY ASTRONOMY. * 

hood of the sun, and it is then but about 4"; showing that tJie 
sun, and not the earth, is the center of its motion. 

The general motion of all the planets, in respect to the stars, 
is direct; that is, eastward; but all the planets that attain op- 
position to the sun, while in opposition, and for some time 
before and after opposition, have a retrograde motion — and 
those planets which show the greatest change in apparent 
diameter, show also, the greatest amount of retrograde motion 
— and all the observed irregularities are systematic in their 
irregularities, showing that they are governed, at least, by 
constant and invariable laws. If the earth is really stationary, 
we cannot account for this retrograde motion of the planets, 
unless that motion is real ; and if real, why, and how can it 
change from direct to stationary, and from stationary to retro- 
grade, and the reverse? 

But if we conceive the earth in motion, and going the same way 
with the planet, and moving more rapidly than the planet, then the 
planet xvill appear to nm back ; that is, retrograde. 

And as this retrogradation takes place with every planet, 
when the earth and planet are both on the same side of the 
sun, and the planet in opposition to the sun ; and as these cir- 
cumstances take place in all positions from the sun, it is a suf- 
ficient explanation of these appearances ; and conversely, then, 
these appearances show the motion of the earth in an orbit 
round the sun. 

When a planet appears to be stationary, it must be really so, 
or be moving directly to or from the observer. And if it be 
moving to or from the observer, that circumstance will be 
indicated by the change in apparent diameter ; and observa- 
tions confirm this, and show that no planet is really stationary, 
although it may appear to be so. 

If we suppose the earth to be but one of a family of bodies, 
called planets — all circulating round the sun at different 

When do planets appear to retrograde ? When a planet appears to be 
stationary, is it really so ? What supposition is here made in respect to the 
earth ? 



APPARENT MOTIONS OF THE PLANETS. 105 

times — in the order of Mercury, Venus, Earth, Mars, (omitting 
the small telescopic planets), Jupiter, Saturn, Herschel, or 
Uranus, we can then give a rational and simple account for 
every appearance observed, and without discussing the ancient 
objections to the true theory of the solar system, we shall 
adopt it at once, and thereby save time and labor, and intro- 
duce the reader into simplicity and truth. 

This, the true solar system, as now known and acknowledged, 
is called the Copernican system, from its discoverer, Coperni- 
cus, a native of Prussia, who lived some time in the fifteenth 
century. 

But this theory, simple and rational as it now appears, and 
capable of solving every difficulty, was not immediately adop- 
ted ; for men had always regarded the earth as the chief object 
in God's creation ; and consequently man, the lord of creation, 
a most important being. But when the earth was hurled from 
its imaginary, dignified position, to a more humble place, it 
was feared that the dignity and vain pride of man must fall 
with it ; and it is probable that this was the root of the oppo- 
sition to the theory. 

So violent was the opposition to this theory, and so odious 
would any one have been who had dared to adopt it, that it 
appears to have been abandoned for more than one hundred 
years, and was revived by Galileo about the year 1620, who, 
to avoid persecution, presented his views under the garb of a 
dialogue between three fictitious persons, and the points left 
undecided. But the caution of Galileo was not sufficient, or 
his dialogue was too convincing, for it woke up the Inquisition, 
and he was forced to sign a paper denouncing the theory as 
heresy, on the pain of perpetual imprisonment. 

Thus, persecuting error, has always moved in advance of 
truth, and though powerful, it can never be finally successful. 

Who discovered the true solar system ? Give a brief outline of the Co- 
pernican system ? Why did men so violently oppose this system ? How 
long was this system lost, and how can we account for its being neglected 
and abandoned? Who revived it? What trouble did this bring on that 
Philosopher ? 



106 



ELEMENTARY ASTRONOMY. 



CHAPTER VI. 

THE COPERNICAN SYSTEM ILLUSTRATED. 

The following figure is designed to be a partial representa- 
tion of the solar system. The center is the locality of the 
Sun, and the innermost circle represents the orbit of Mercury, 
the second circle the orbit of Venus, the third circle the orbit 
of the Earth, and the outermost circle represents the orbit of 
Mars. 




Whereabouts in the solar system is the sun located ? What orbit is 
nearest to the sun ? What orbit does the third circle represent ? 



THE COPERNICAN SYSTEM ILLUSTRATED. 107 

There is not space on the page to represent the orbit of the 
planets, beyond or more remote from the sun than Mars, and, 
indeed, there is not space to represent these in due proportion, 
on a scale of sufficient magnitude. 

Far, far away beyond the orbits of the planets are the fixed 
stars — so far, that the whole solar system is but a point in 
comparison. To help the imagination, we have represented 
stars about the borders of the figure. 

Let a, b, c, d, &c. be the direct course of the planets in the 
heavens, and suppose E to be the position of the earth at some 
particular time ; then we know that those stars, a little in ad- 
vance of g, will come to the meridian at midnight, and the sun 
is in the direction of the stars, near b, directly opposite. Let 
H be the position of Mars, and Fthe position of Venus. The 
line from E to M, extended to the stars, will show the position 
of Mars among the stars ; and a line from E to V shows the 
position of Venus among the stars at /. Now suppose the 
earth to move from E to E, , and during the same time Venus 
must move through a larger arc, as from Fto F",, and Mars 
move through a lesser arc, as from M to J/, . Now Mars appears 
to have gone backward among the stars, and Venus to have 
moved a little in advance, and S the center of the sun, is the 
only point in the solar system from which the motion of the 
planets can appear uniform as to velocity or direction. 

When the earth is at E\ , and Mars at M { , as here repre- 
sented the apparent diameter of Mars is greatest, and when 
Mars is in its orbit beyond the sun, its apparent diameter is 
least, as was noticed in the preceding chapter. Indeed, it was 
appearances, or rather, observations, that established this 
theory of the solar system. 

Mercury and Venus, never coming in opposition to the sun, 
but revolving around that body in orbits that are within that 
of the earth, are therefore called inferior planets. 

"Why are Mercury and Venus called inferior planets ? Why are all 
others called superior planets ? To the inhabitants of Mars is the Earth 
an inferior or a superior planet ? 



108 



ELEMENTARY ASTRONOMY. 



Those that come in opposition, and thereby show that their 
orbits are outside of the earth, are called superior planets. 

We shall show how to investigate and determine the position 
of one inferior planet ; and the same principles will be suffi- 
cient to determine the position of any inferior planet. 

It will be sufficient, also, to investigate and determine the 
orbit of one superior planet ; and, if that is understood, it may 
be considered as substantially determining the orbits of all the 
superior planets ; and after that, it will be sufficient to state 
results. 

For materials to operate with, we give the following table of 
the planetary irregularities, (so called,) drawn from obser- 
vation : v 



Planets. 



Mercury, 

Venus, 

Earth, 

Mars, 

Jupiter, 

Saturn, 

Uranus, 



Greatest 
Apparent 
Diameters. 



11.3 
59.6 

17.1 

44.5 

20.1 

4.1 



Least 

Apparent 

Diameters. 



5.0 
9.6 

3.6 
30.1 
16.3 

3.7 



Angular Distance 
from Sun at the 
instant of being 
stationaiy. 

O / 

18 00 
28 48 

136 48 
115 12 
108 54 
103 30 



Mean arc of 
Retrogradation . 


O / 
13 30 
16 12 

16 12 
9 54 
6 18 
3 36 



On the supposition, however, that the planets revolve in 
circles (which is not far from the truth), the greatest and least 
apparent diameters furnish us with sufficient data to compute 
the distances of the planets from the sun in relation to the dis- 
tance of the earth, taken as unity. 

In addition to the facts presented in the preceding table, we 
must not fail to note the important element of the elongations 
of Mercury and Venus. This term can be applied to no other 
planets. 

It is very variable in regard to Mercury — showing that the 
orbit of that planet is quite elliptical. The variation is much 

What observations will furnish means to determine the relative distances 
of the planets from the sun ? How is it known that the orbit of Mercury 
is more elliptical than that of Venus ? 



THE COPERNICAN SYSTEM ILLUSTRATED. 109 

less in regard to Venus, showing that Venus moves round the 
sun more nearly in a circle. 

For Mercury. For Venus. 

The least extreme elongation, 17° 37' 44° 58' 

The greatest " " 28° 4' 47° 30' 

The mean elongation, 22° 46' 46° 20' 

Relying on these facts as established by observations, we 
can easily deduce the relative orbits of Mercury and Venus. 

Let S represent the sun, 
E the earth, V Venus. 

Conceive the planet to 
pass round the sun in the 
direction of A VB. 

The earth moves also in 
the same direction, but 
not so rapidly as Venus. 

Now it is evident from 
inspection, that when the 
planet is passing by the 
earth, as at J3, it will ap- 
pear to pass along in the 
heavens in the direction of 
m to n. But when the 
planet is passing along in 
its orbit, at A, and the earth about the position of E, the 
planet will appear to pass in the direction of n to m. When 
the planet is at V, as represented in the figure, its absolute 
motion is nearly toward the earth, and, of course, its appear- 
ance is nearly stationary. 

It is absolutely stationary only at one point, and even then 
but for a moment ; and that point is where its apparent motion 
changes from direct to retrograde, and from retrograde to di- 

When does the motion of the inferior planets appear most direct ? When 
most retrograde ? When stationary ? Do the planets appear st at ion avy 
for any considerable time? 




110 ELEMENTARY ASTRONOMY. 

rect ; which takes place when the angle SEV is about 29 
degrees on each side of the line SE. 

When the line EV touches the circumference AVB, the 
angle SEV, or angle of elongation, is then greatest; and the 
triangle SEV is right angled at V; and if SE is made radius, 
SV will be the sine of the angle SEV. 

But the line SE is assumed equal to unity, and then £ J 7 " will 
be the natural sine of 46° 20', and can be taken out of any- 
table of natural sines ; or it can be computed by logarithms, 
and the result is .72336. 

For the planet Mercury, the mean of the same angle is 22° 
46, and the natural sine of that angle, or the mean radius of 
the planet's orbit, is .38698. 

Thus we have found the relative mean distances of three 
planets from the sun, to stand as follows : 

Mercury, 0.38698 

Venus, 0.72336 

Earth, 1.00000 

If the orbits were perfect circles, then the angle SEV of 
greatest elongation, would always be the same ; but it is an 
observed fact that it is not always the same ; therefore the orbits 
are not circles ; and when SVis least, and SE greatest, then 
the angle of elongation is least; and conversely, when /S'F'is 
greatest and SE least, then the angle of elongation is the 
greatest possible ; and by observing in what parts of the heavens 
the greatest and least elongations take place, we can approxi- 
mate to the positions of the longer axis of the orbits. 

By means of the apparent diameters, we can also find the 
approximate relations of their orbits. For instance, when the 
planet Venus is at B, and appears on the sun's disc, its appa- 
lent diameter is 59".6 ; and when it is at A, or as near A as 
can be seen by a telescope, its apparent diameter is 9".6. Now 
put 

SB=x; then EB=l—x; and AE=l+x. 

If the greatest elongation of a planet were always the same, what would 
that circumstance show ? 



THE COPERNICAtf SYSTEM ILLUSTRATED. Ill 

By Art. 66, \—x : 1-fz : : 96 : 596 ; 

Hence, 2=0.72254. 

By a like computation, the mean distance of Mercury from 
the sun is 0.3864. 

To obtain the relative distance of Mars from the sun, we 
proceed as follows : 

Let x be the distance sought ; then when the planet is nearest 
to the earth, its distance must be expressed by (x — 1), and 
when at its greatest distance by (x-\-l); and these quantities 
must be to each other, inversely, as the observed diameters; 
that is, we have the following proportion ; 

x— 1 : z-f-1 : : 3.6 : 17.1. 

Whence x= 1.53333. 

In like manner we may obtain the relative distance of any 
other planet from the sun. 

The next step in the path of astronomical knowledge is to 
determine what observations are necessary to find the periodical 
revolutions of the planets around the sun If observers on 
the earth were at the center of motion, they could determine 
the times of revolution by simple observation. But as the 
earth is one of the planets, and all observers on its surface are 
carried with it, the observations here made must be subjected 
to mathematical corrections, to obtain true results ; and this 
was an impossible problem to the ancients, as long as they 
contended for a stationary earth. 

If the observer could view the planets from the center of 
the sun, he would see them in their true places among the 
stars — and there are only two positions in which an observer 
on the earth will see a planet in the same place as though he 
viewed it from the center of the sun, and these positions are 
conjunction and opposition. 

By what means can astronomers obtain the relative distances of the 
superior planets from the sun ? What is the next step in astronomical 
knowledge ? Why cannot the periodical revolutions of the planets be 
observed directly? 



112 



ELEMENTARY ASTRONOMY. 



Thus, when the earth is at E, and the planet at M, the 
planet is in opposition to the sun ; and it is seen projected 
among the stars at the same point, whether viewed from S or 
from E. 

The time that any planet comes in opposition to the sun, can 
be very distinctly determined by observation. Its longitude 
is then 180 degrees from the longitude of the sun, and comes 
to the meridian nearly or exactly at midnight. If it is a little 
short of opposition at the time of one observation, and a little 
past at another, the observer can proportion to the exact time 
of opposition, and such time cau be definitely recorded — and 
by such observation, we have the true position of the planet, 
as seen from the sun. 

Now suppose the planet 
at Eio pass on and make 
a revolution, and when it 
comes round to E again, 
the planet M is near m, 
and the planet at E has to 
pass on to E i before the 
planet is again in opposi- 
tion to the sun. 

During this time, the 
earth, or inferior planet, must 
describe one revolution, and 
the arc MSm, and the supe- 
rior planet must describe 
the excess arc MSm. 

The time from one of 
these oppositions of the same planet to another, is called the 
synodic revolution of the planet, and observations have furnished 
us with the facts as stated in the following table : 




When can we see a planet in the same position among the stars as though 
it were seen from the center of the sun? What is understood by the synod - 
ical revolution of a planet ? 



THE COPERNICAN SYSTEM ILLUSTRATED. 



113 





Mean Duration of 


f Mean Duration of the Synodic 


Planets. 


the Retrograde 


Revolution, or interval between 




motion. 


two successive oppositions. 


Mercury, 


23 days. 


118 days. 


Venus, 


42 " 


584 " 


Earth, 






Mars, 


75 " 


780 " 


Jupiter, 


121 " 


399 « 


Saturn, 


139 " 


378 " 


Uranus, 


151 " 


370 <« 



In the preceding table, the word mean is used at the head of 
the several columns, because these elements are variable — some- 
times more, and sometimes less, than the numbers here given 
— which indicate that the planets do not revolve in circles 
round the sun, but most probably in ellipses, like the orbit of 
the earth. 

Let us now take the time of the synodic revolution of Jupi- 
ter, from the above table, and from it determine the periodical 
revolution of that planet. In 365.256 days the earth describes 
a revolution, or 360°, at an average rate of 59' 8" per day. 
From 399 days subtract 365.256 days, and the difference is 
33.744 days. In 33.744 days at 59' 8" per day, the earth will 
describe 33°.256, which is the arc that Jupiter describes in 
399 days, as seen from the sun. How many days then will be 
required by that planet to describe 360°? The proportion 
stands thus : 

33°.256 : 360° : : 299 : the time required. 

This proportion gives a little over 4319 days for the sidereal 
revolution of Jupiter. The true time is a little over 4332 days, 
the cause of the difference will soon be explained. 

Let us now determine, approximately, the sidereal revolution 
of Venus. 

Its synodic revolution is put down at 584 days. In this time 
the earth describes (575.58) degrees, but because Venus is an 
inferior planet, it describes one revolution more. Therefore Venus 



Why do astronomers use the word mean, so often? In a synodic revo- 
lution, how many degrees does one planet describe more than the other? 
Which one describes the greatest number of degrees? 
10 



114 ELEMENTARY ASTRONOMY. 

must describe 935.53 degrees in 584 days. In what time then 
will that planet describe 360 degrees? 
The proportion is this : 

935 ,-W : 360 : : 584 : the time sought. 

The result of this proportion gives 224^ days for the side- 
real revolution of Venus, which is very near the truth. 

All these results are, of course, understood as first approxi- 
mations, and accuracy here is not attempted. "We are only 
showing principles ; and it will be noticed, that the times here 
taken in these computations, are only to the nearest days, and 
not fractions of a day, as would be necessary for accurate 
results. By this method, accuracy is never attained, on 
account of the eccentricities of the orbits. No two synodical 
revolutions are exactly alike ; and therefore it is very difficult 
to decide what the real mean values are. 

To obtain accuracy, in astronomy, observations must be 
carried through a long series of years. The following is an 
example : and it will explain how accuracy can be attained in 
relation to any other planet. 

On the 7th of November, 1631, M. Cassini observed Mercury 
passing over the sun ;* and from his observations then taken, 
deduced the time of conjunction to be at 7h. 50m., mean time, 
at Paris, and the true longitude of Mercury 44° 41'' 35". 

Comparing this occultation with that which took place in 
1723, the true time of conjunction was November 9th, at 5h. 
29m. p. m., and Mercury's longitude was 46° 47' 20". 

The elapsed time was 92 years, 2 days, 9 hours, 39 minutes. 

* The times "when Mercury and Venus are seen in the same part of the 
heavens from the sun as from the earth, can only be observed from the earth 
when these planets are in a line between the earth and some part of the 
sun. The planet will then appear on the sun as a black spot,and then it is 
called an occultation. 

Why is accuracy as to the times of revolution of the planets never at- 
tempted to be deduced from a synodic revolution? How then is accuracy 
attained ? Why did the author introduce a method that could not be relied 
upon for accuracy? 



THE COPERNICAN SYSTEM ILLUSTRATED. 115 

Twenty-two of these years were bissextile ; therefore the 
elapsed time was (92X365) days, plus 24d. 9h. 39m. 

In this interval, Mercury made 382 revolutions, and 2° 5' 
45" over. That is, in 33604.402 days, Mercury described 
137522.095826 degrees ; and therefore, by division, we find 
that in one day it would describe 4°. 0923, at a mean rate. 

Thus, knowing the mean daily rate to great accuracy, the 
mean revolution, in time, must be expressed by the fraction 

■ 36Q =87.9701 days, or 87 days 23 h. 15 m. 57 s. 
4.0923 J J 

The following is another method of observing the periodical 
times of the planets, to which we call the student's special attention. 

The orbits of all the planets are a little inclined to the plane 
of the ecliptic. 

The planes of all the planetary orbits pass through the center 
of the sun ; the plane of the ecliptic is one of them, and there- 
fore the plane of the ecliptic and the plane of any other planet 
must intersect each other by some line passing through the 
center of the sun. The intersection of two planes is always a 
straight line. (See Geometry.) 

The reader must also recognize and acknowledge the follow- 
ing principle : 

That a body cannot appear to be in the plane of an observer, un- 
less it really is in that plane. 

For example : an observer is always in the plane of his 
meridian, and no body can appear to be in that plane unless it 
really is in that plane ; it cannot be projected in or out of that 
plane, by parallax or refraction. 

Hence, when any one of the planets appears to be in the 
plane of the ecliptic, it actually is in that plane ; and let the 
time be recorded when such a thing takes place. 

The planet will immediately pass out of the plane, because 
the two planes do not coincide. Passing the plane of the 

Do the planets appear to pass along in the heavens in the plane of the 
ecliptic? Can a planet appear to be in the ecliptic unless it is really in 
that place ? 



116 ELEMENTARY ASTRONOMY. 

ecliptic is called passing the node. Keep track of the planet 
until it comes into the same plane ; that is, crosses the other 
node: in this interval of time the planet has described just 
180°, as seen from the sun (unless the nodes themselves are in 
motion, which in fact they are ; but such motion is not sensible 
for one or two revolutions of Yenus or Mars.) 

Continue observations on the same planet, until it comes into 
the ecliptic the second time after the first observation, or to 
the same node again ; and the time elapsed, is the time of a revo- 
lution of that planet round the sun. From such observations the 
periodical time of Venus became well known to astronomers, 
long before they had opportunities to decide it by comparing 
its transits across the sun's disc ; and by thus knowing its 
periodical time and motion, they were enabled to calculate the 
times and circumstances of the transits which happened in 
1761, and in 1769 ; save those resulting from parallax alone. 

From observations long continued and accurately made, the 
following results were long since established : 

Sidereal Revolutions. Mean distances from ||| 

Mercury, - - 87.969258 0.387098 

Venus, - - 224.700787 0.723332 

Earth, - - - 365.256383 1.000000 

Mars, - - 686.979646 1.523692 

Jupiter, - - 4332.584821 5.202776 

Saturn, - - 10759.219817 9.538786 

Uranus, - 30686.820830 19.182390 

By inspecting this table, we shall perceive that the greater 
the distance from the sun the greater the time of revolution, 
but the increase of the times of revolution is much greater 
than the increase of distances. This shows that the greater 
the distance a planet is from the sun, the slower is its actual 
motion .* 

* Let the reader be careful not to confound real or actual motion with 
angular motion. 

By what observation can the periodical revolution of a planet be observed 
directly ? Do the times of revolution, and the distances from the sun, in- 
crease in the same ratio? 



THE COPERNICAN SYSTEM ILLUSTRATED. 117 

Kepler, a Danish philosopher, about the year 1617, after 
various comparisons of the increase of time with the increase 
of distance, found that the square of the revolution corres- 
ponded to the cube of the distance, and thus established his 
third law. 

We may now recapitulate the three laws of the solar system, 
called Kepler's laws. 

1st. The orbits of the planets are ellipses, of which the sun 
occupies one of the foci. 

2d. The radius vector in each case describes areas about the 
focus, which are proportional to the times. 

3d. The squares of the times of revolution are to each other as 
the cubes of the mean distances from the sun. 

The first of these laws is nothing more than an observed 
fact : — the second and third are also observed facts, and are 
susceptible of mathematical demonstration on philosophical 
principles, as may be seen in our University Edition of As- 
tronomy, and in our Mathematical Sequel. 

Kepler's third law is of great practical utility in finding the 
mean distances of any newly discovered planets from the sun. 

Thus, suppose a new planet should be discovered, whose 
time of revolution round the sun was just five years, what 
would be its mean distance from the sun ? 

Let x represent the distance sought. 

Then l 2 : 5 2 : : l 3 : a; 3 . 

Whence rr 3 =25, or #=2:924. 

That is, the distance of that planet from the sun must be 
2.924 times the distance between the sun and the earth. 

Repeat Kepler's laws. Make a proportion with the numbers taken from 
the table, to show that you understand the enunciation of the third law. 



1 18 ELEMENTARY ASTRONOMY. 



CHAPTER VII. 



THE TRANSITS OF VENUS AND MERCURY — THE SUN'S 

HORIZONTAL PARALLAX — THE REAL MAGNITUDE 

AND DISTANCE TO THE SUN. 

We have thus far been very patient in our investigations — 
groping along — finding the form of the planetary orbits, and 
their relative magnitudes ; but, as yet, we know nothing of the 
distance to the sun, save the indefinite fact, that it must be 
very great, and its magnitude great ; but how great, we can 
never know, without the sun's parallax. Hence, to obtain 
this element, has always been an interesting problem to as- 
tronomers. 

The ancient astronomers had no instruments sufficiently 
refined to determine this parallax by direct observation, in the 
manner of finding that of the moon, and hence the ingenuity 
of men was called into exercise to find some artifice to obtain 
the desired result. 

After Kepler's laws were established, and the relative dis- 
tances of the planets made known, it was apparent that their 
real distance could be deduced, provided, the distance between 
the earth and any planet could be made known. 

The relative distances of the earth and Mars, from the sun 
(as determined by Kepler's law) are as 1 to 1.5237 ; and hence 
it follows that Mars, in its oppositions to the sun, is but about 
one half as far from the earth as the sun is ; and therefore its 
parallax must be about double that of the sun ; and several 
partially successful attempts were made to obtain it by obser- 
vations. 

On the 15th of August, 1719, Mars being very near its 
opposition to the sun, and very near a star of the 5th magni- 
tude, its parallax became sensible ; and Mr. Maraldi, an Italian 

When Mars is in opposition to the sun, how much greater is its parallax 
than the parallax of the sun? 



SOLAR PARALLAX. 119 

astronomer, pronounced it to be 27". The relative distance of 
Mars, at that time, was 1 .37, as determined from its position 
and the eccentricity of its orbit. 

But horizontal parallax is the angle under which the semi- 
diameter of the earth appears ; and, at a greater distance, it will 
appear under a less angle. The distance of Mars from the 
earth, at that time, was .37, and the distance of the sun was 1 ; 

Therefore, I : .37 : : 27" : 9".99, or 10" nearly, 
for the sun's horizontal parallax. 

On the 6th of October, 1751, Mars was attentively observed 
by Wargentin and Lacaille (it being near its opposition to the 
sun), and they found its parallax to be 24".6, from which they 
deduced the mean parallax of the sun, 10".7. But at that time, 
if not at present, the parallax of Mars could not be observed 
directly, with sufficient accuracy to satisfy astronomers ; for no 
observer could rely on an angular measure within 2". 

Not being satisfied with these results, Dr. Halley, an English 
astronomer, very happily conceived the idea of finding the sun's 
parallax by the comparisons of observations made from different 
parts of the earth, on a transit of Venus over the sun's disc. 
If the plane of the orbit of Venus coincided with the orbit of 
the earth, then Venus would come between the earth and sun 
at every inferior conjunction, at intervals of 584.04 days. But 
the orbit of Venus is inclined to the orbit of the earth by an 
angle of 3° 23' 28"; and, in the year 1800, the planet crossed 
the ecliptic from south to north, in longitude 74° 54' 12", and 
from north to south, in longitude 254° 54' 12": the first men- 
tioned point is called the ascending node; the last, the descending 
node. The nodes retrograde 31' 10" in a century. 

The mean synodical revolution of 584 days corresponds with 
no aliquot part of a year; and therefore, in the course of time, 
these conjunctions will happen at different points along the 
ecliptic. The sun is in that part of the ecliptic near the nodes 

Who conceived the idea of deducing the sun's parallax from a transit of 
Venus? Why is there not a transit at every inferior conjunction of Venus 
with the sun? 



120 ELEMENTARY ASTRONOMY. 

of Venus, June 5th and December 6th or 7th ; and the two last 
transits happened in 1761 and 1769 ; and from these periods we 
date our knowledge of the solar parallax. 

The periodical revolution of the earth is 365.256383 days, 
and that of Venus is 224.700787 days ; and as numbers they 
are nearly in proportion of 13 to 8; more nearly as 382 to 235. 

From this it follows, that eight revolutions of the earth re- 
quire nearly the same time as thirteen revolutions of Venus ; 
and, of course, whenever a conjunction takes place, eight years 
afterward, another conjunction will take place very near the 
same point in the ecliptic. 

If the proportional revolutions were exactly as 13 to 8, then 
the conjunctions at these periods would always take place 
exactly in the same point in the heavens ; but as it is, conjunc- 
tions take place east and west of that point, and approximate 
nearer to it in periods more nearly proportional to the revolu- 
tion of the planets. 

To be more practical, however, the intervals between con- 
junctions are such, combined with a slight motion of the nodes, 
that the geocentric latitude of Venus, at inferior conjunctions 
near the ascending node, changes about 19' 30" to the north, 
in a period of about eight years. At the descending node, it 
changes about the same quantity to the southward, in the same 
period ; and as the disc of the sun is but little over 32', it is 
impossible that a third transit should happen sixteen years after 
the first ; hence, only two transits can happen, at the same 
node, separated by the short interval of eight years. 

If at any transit we suppose Venus to pass directly over the 
center of the sun, as seen from the center of the earth — that 
is, pass conjunction and node at the same time — at the end of 
another period of about eight years, Venus would be 19' 30" 
north or south of the sun's center; but as the semi-diameter 
of the sun is but about 16', no transit could happen in such a 

If Venus should pass over the center of the sun at any inferior conjunc- 
tion, should we have another transit in eight years after? How far would 
Venus then pass from the limb of the sun ? 



SOLAR PARALLAX. 121 

case ; and there would be but one transit at that node until 
after the expiration of a long period of 235 or 243 years. 

After passing the period of eight years, we take a lapse of 
105 or 113 years, or thereabouts, to look for a transit at the 
other node. 

Knowing the relative distances of Venus, and the earth, from 
the sun — the positions and eccentricities of both orbits — also 
their angular motions and periodical revolutions — every cir- 
cumstance attending a transit, as seen from the earth's center, 
can be calculated; and Dr. Halley, in 1677, read a paper be- 
fore the London Astronomical Society, in which he explained 
the manner of deducing the parallax of the sun from observa- 
tions taken on a transit of Yenus or Mercury across the sun's 
disc, compared with computations made for the earth's center, 
or by comparing observations made on the earth at great dis- 
tances from each other. 

The transits of Venus are much better, for this purpose, 
than those of Mercury ; as Venus is larger, and nearer the 
earth, and its parallax at such times much greater than that of 
Mercury ; and so important did it appear, to the learned world, 
to have correct observations on the last transit of Venus, in 
1769, at remote stations, that the British, French, and Russian 
governments were induced to send out expeditions to various 
parts of the globe, to observe it. " The famous expedition of 
Captain Cook, to Otaheite, was one of them." 

The mean result of all the observations made on that mem- 
orable occasion, gave the sun's parallax, on the day of the 
transit, (3d of June,) 8".5776. The horizontal parallax, at 
mean distance, may be taken at 8".6 ; which places the sun, at 
its mean distance, no less than 23984 times the length of the 
earth's semi-diameter, or about 95 millions of miles. 

This problem of the sun's horizontal parallax, as deduced 
from observations on a transit of Venus, we regard as the most 

Why are transits of Venus better for this object than those of Mercury? 
What is the amount of the sun's parallax ? What is then the distance to 
the sun, in miles ? 
11 



122 



ELEMENTARY ASTRONOMY. 



important, for a student to understand, of any in astronomy ; 
for without it, the dimensions of the solar system, and the 
magnitudes of the heavenly bodies, must be taken wholly on 
trust ; and we have often protested against mere facts being 
taken for knowledge. 

We shall now attempt to explain this whole matter on gen- 
eral principles, avoiding all the little minutiae which render the 
subject intricate and tedious ; for our 
only object is to give a clear idea 
of the nature and philosophy of the 
problem. 

Let S represent the sun, and m n and 
PQ small portions of the orbits of 
Venus, and the earth. 

As these two bodies move the same 
way, and nearly in the same plane, we 
may suppose the earth stationary, and 
Venus to move with an angular velocity 
equal to the difference of the two. 

When the planet arrives at v , an ob- 
server at G would see the planet pro- 
jected on the sun, making a dent at v'. 
But an observer at A would not see 
the same thing until after the planet 
had passed over the small arc vq, with 
a velocity equal to the difference be- 
tween the angular motion of the two 
bodies ; and as this will require quite 
an interval of absolute time, it can be 
detected; and it measures the angle 
Av'G; an angle under which a definite portion of the earth 
appears as seen from the sun. 

To have a more definite idea of the practicability of this 



If two observers are at a distance from each other, will they see the be- 
ginning or end of the transit at the same time? Is it the object of the 
observations to determine the difference in the time ? 



SOLAR PARALLAX. 123 

method, let us suppose the parallactic angle, Av'G, equal to 
10", and inquire how long Yenus would be in passing the rela- 
tive arc vq. 

Venus, at its mean rate, passes - 1° 36' 8" in a day. 

The earth, " " " - - 59' 8" " 

The relative, or excess motion of Venus for a mean solar 
day, is then 37'. 

Now as 37' is to 24h. so is 10" to a fourth term ; or as 
2220" : 1440m. : : 10" : 6m. 29s. 

Now if observation had given more than 6 minutes and 29 
seconds, we should conclude that the parallactic angle was 
more than 10"; if less, less. But this is an abstract proposition. 
When treating of an actual case in place of the mean motion, 
we must take the actual angular motions of the earth and Venus 
at that time, and we must know the actual position of the ob- 
servers A and G in respect to each other, and the position of 
each in relation to a line joining the center of the sun ; and 
then by comparing the local time of observation made at A, 
with the time at G, and referring both to one and the same 
meridian, we shall have the interval of time occupied by the 
planet in passing from v to q, from which we deduce the paral- 
lactic angle Av'G, and from thence the horizontal parallax, or 
the magnitude that the angle Av'G would be, in case the dis- 
tance A G were equal to the semi-diameter of the earth. 

The same observations can be made when the planet passes 
off the sun, and a great many stations can be compared with 
A, as well as the station G. In this way, the mean result of 
a great many stations was found in 1761, and in 1769, and the 
mean of all cannot materially differ from the truth. 

The first transit known to have been observed was in 1 639, 
December 4th; to this add 225 years, and we have the time of 
the next transit, at the same node, 1874, December 8th; and 
eight years after that will be another, 1882, December 6th. 

Has the parallax of the sun "been deduced from one observation, or is it 
the result of many? Can this result be far from the truth? When will 
the nest transit occur? 



124 ELEMENTARY ASTRONOMY. 



CHAPTER VIII 



TO FIND THE DIAMETER AND MAGNITUDE OF 
A PLANET. 

Having now found the solar horizontal parallax, and conse- 
quently the real distance to the sun, we have sufficient data to 
tind the real distance, diameter, and magnitude of each and 
every planet in the solar system. 

Let the reader bear in mind that the horizontal parallax of 
any body is the angle under which the semi-diameter of the 
earth appears, as seen from that body. The apparent semi- 
diameter of the body, and the earth's horizontal parallax, as 
seen from that body, is one and the same thing ; therefore, 
As the diameter of the earth 
Is to the diameter of any other planet, 
So is the horizontal parallax of the planet 
To its apparent semi- diameter. 
The mean horizontal parallax of the sun, as determined by 
the transit of Venus, is 8".6, and the semi-diameter of the sun 
at the corresponding mean distance, is 16' 1", or 961". Now 
let d represent the real diameter of the earth, and D that of 
the sun, then we shall have the following proportion : 

d : D : : 8".6 : 961".0 
But d is 7912 miles ; and the ratio of the last two terms is 
111.66; therefore 2>=(111.66)(7912)==883454 miles. 

The sun's horizontal parallax is the angle at the vertex of 
a right angled triangle, and the base opposite, is the semi- 
diameter of the earth ; and if we call that distance unity, and 
compute the distance of one of the other sides by trigonometry, 
we shall find it equal to 23984 units, or semi-diameters of the 

What element must astronomers obtain before they can determine the 
magnitudes and distances of the planets? State the rule to find the diam- 
eter of the sun or a planet ? 



DIAMETERS AND MAGNITUDES OF THE PLANETS. 125 



earth ; but to aid the memory, we may say that the distance is 
24000 times the earth's semi-diameter. 

If we change the unit, from the semi-diameter of the earth, to 
an English mile, then the mean distance between the earth and 
sun must be 

(3956)(24000)==94.944000 miles. 
■ In round numbers we may say 95 millions of miles. 

By Kepler's third law, we know the relative distances of 
the planets from the sun, and now knowing the real distance, 
in miles, of one of them (the earth), we can determine the real 
distances of the others by multiplying each relative distance 
by 94.944000. 

Relative distances. True distances. 



Mercury, 


- 0.3871 ' 




r 36.752.822 


Venus, - 


- 0.7233 




68.672.995 


Earth, - - 


1.0000 


94.944000= 


94.944.000 


Mars, 


1.5237 


" . H 


144.666.172 


Jupiter, 


- 5.2028 




493.974.643 


Saturn, - 


- 9.5388 




905.651.827 


Uranus, - 


19.1824 \ 




.1814.417.800 



By observations taken on the transit of Venus, in 1769, it 
was concluded that the horizontal parallax of that planet was 
30".4 ; and its semi-diameter, at the same time, was 29".2. 
Hence, 304 : 292 : : 7912 : to a fourth term; which gives 
7599 miles for the diameter of Venus. 

We cannot observe the horizontal parallax of Jupiter, Saturn, 
or any other very remote planet : if known at all, it becomes 
known by computation ; but the parallax of the sun being now 
known, and the relative distances of the earth and all the 
planets from the sun being known, the horizontal parallax of 
any planet can be computed as follows. Once mvre we remind 
the reader that the sun's horizontal parallax is the angle uuder 
which the earth appears, as seen from the sun — seen from a 

What is the multiplier to the relative distances of the planets from the 
sun, to obtain the distances in miles? Do we observe the horizontal paral- 
lax of a remote planet, or compute it ? 



126 ELEMENTARY ASTRONOMY. 

greater distance, the angle must be proportionally less. Seen 
from a distance equal to the mean distance of Jupiter from the 

o" o 

sun, the angle would be This, then, is the horizontal 

b 5.2028 

parallax of Jupiter, when Jupiter is at a distance from the earth 
equal to the mean distance of Jupiter from the sun. The appa- 
rent semi-diameter of Jupiter, when at the same distance, as 
determined by observation, is 18".35 ; therefore the diameter of 
Jupiter can be determined by the following proportion 

7912 : D : : 8 ' 6 : 18.35, 
5.2028 

in which D represents the magnitude sought. 

Whence i>= 7912 >< 18 - 35 -><JJgg 8 = 7912Xll.l = 87823 miles 
8.6 

In the same manner we can find the diameter of any other 
planet whose apparent diameter can be distinctly measured, 
and whose relative distance to the sun is known. The diameter 
may also be computed directly by plane trigonometry. 

We have just seen that the diameter of Jupiter is 11.1 times 
the diameter of the earth ; but this is the equatorial diameter 
of the planet. Its polar diameter is less, in the proportion of 
167 to 177, as determined by the mean of many micrometrical 
measurements ; which proportion gives 82930 miles, for the 
polar diameter of Jupiter. These extremes give the mean 
diameter of Jupiter, to the mean diameter of the earth, as 
10.8 to 1. 

But the magnitudes of similar bodies are to one another as 
the cubes of their like dimensions ; therefore the magnitude of 
Jupiter is to that of the earth, as (10. 8) 3 to 1, and from thence 
we learn that Jupiter is 1260 times greater than the earth. 

In this manner are found the magnitudes, distances, velocity, 
&c. &c. of the planets, which appear in tables in various astro- 
nomical works. 

State the proportion to find the diameter of a planet when its horizontal 
parallax and apparent semi-diameter are both known. How much greater 
is the diameter of Jupiter than the earth ? How much greater then is the 
magnitude of Jupiter than that of the earth? 



DESCRIPTION OF THE SOLAR SYSTEM. 127 



CHAPTER IX. 

A GENERAL DESCRIPTION OF THE SOLAR 
SYSTEM. 

The solar system is so called because the sun occupies the 
central position, and apparently holds and governs the motion 
of all the planets which revolve around him. 

We shall commence our description with 

THE SUN. 

This body, as we have seen in the preceding pages, is of 
immense magnitude, much greater than all the planets taken 
together, comparatively stationary, the dispenser of light and 
heat, and apparently at least, the repository of that attractive 
force which holds the system together, and regulates the plan- 
etary motions. 

" Spots on the sun seem first to have been observed in the 
year 1611, since which time they have constantly attracted 
attention, and have been the subject of investigation among 
astronomers/ ' 

A spot first appears on the eastern limb of the sun, and by 
degrees comes forward to the middle, and passes off to the west. 
After being absent about the same length of time, the same 
spot appears in the same place as before, thus indicating a revo- 
lution of the sun on an axis, in 25 days 14 hours, the sy nodical 
revolution of the spots being 27 days 12^- hours. 

These spots change their appearance, "and become greater 
or less, to an observer on the earth, as they are turned to, or 
from him ; they also change in respect to real magnitude and 
number ; one spot, seen by Dr. Herschel, was estimated to be 

Whereabouts in the solar system is the sun ? Does it i-evolve on an axis 
— and if so, how did the fact become known ? TV hat is the time of revo- 
lution ? "What is said of the size of some of these spots ? 



128 ELEMENTARY ASTRONOMY. 

more than six times the size of our earth, being 50000 miles 
in diameter. Sometimes forty or fifty spots may be seen at the 
same time, and sometimes only one. They are often so large 
as to be seen with the naked eye ; this was the case in 1816. 

" In two instances, these spots have been seen to burst into 
several parts, and the parts to fly in several directions, like a 
piece of ice thrown upon the ground. 

"Dr. Herschel, from many observations with his great tel- 
escope, concludes, that the shining matter of the sun consists 
of a mass of phosphoric clouds, and that the spots on his sur- 
face are owing to disturbances in the equilibrium of this lumi- 
nous matter, by which openings are made through it. There 
are, however, objections to this theory, as indeed there are to 
all the others, and at present it can only be said, that no satis- 
factory explanation of the cause of these spots has been given.' * 

MERC URY. 

This planet is the nearest to the sun, and has been the sub- 
ject of considerable remark in the preceding pages. It is 
rarely visible, owing to its small size and proximity to the sun, 
and it never appears larger to the naked eye than a star of the 
fifth magnitude. 

Mercury is seen through a telescope sometimes in the form 
of a half moon, and sometimes a little more or less than half 
its disc is seen ; hence it is inferred, that it has the same phases 
as the moon, except that it never appears quite round, because 
its enlightened side is never turned directly towards us, unless 
when it is so near the sun as to become invisible, by reason 
of the splendor of the sun's rays. The enlightened side of 
this planet being always towards the sun, and its never appear- 
ing round, are evident proofs that it shines not by its own 
light; for, if it did, it would constantly appear round. The 
best observations of this planet are those made when it is 
seen on the sun's disc, called its transit ; for in its lower con- 
How large does Mercury appear ? What is its position when the best 
observations can be made on it ? 



DESCRIPTION OF THE SOLAR SYSTEM. 129 

junction, he sometimes passes before the sun, like a little spot, 
eclipsing a small part of the sun's body. 

Mercury is too near the sun to admit of any observations on 
the spots on its surface ; but its period of rotation has been 
determined by the variations in its horns — the same ragged 
corner comes round at regular intervals of time — 24h. 5m. 

The best time to see Mercury, in the evening, is in the spring 
of the year, when the planet is at its greatest elongation east of 
the sun. It will then be visible to the naked eye about fifteen 
minutes, and will set about an hour and fifty minutes after the 
sun. When the planet is west of the sun, and at its greatest 
distance, it may be seen in the morning, most advantageously 
in August and September. The symbol for the greatest elon- 
gation of Mercury, as written in the common almanac, is § Gr. 
Elon. 

VENUS. 

This planet is second in order from the sun, and in relation 
to its position and motion, it has been sufficiently described. 
The period of its rotation on its axis is 23h. 21m. The position 
of the axis is always the same, and is not at right angles to the 
plane of its orbit, which gives it a change of seasons. The 
tangent position of the sun's light across this planet shows a 
very rough surface ; indeed, high mountains. By the radiating 
and glimmering nature of the 
light of this planet, we infer 
that it must have a deep and 
dense atmosphere. 

These figures present a tele- 
scopic view of this planet ; the 
narrow crescent appears when 
the planet is near its inferior conjunction, the other when the 
planet is near its greatest elongation. 

The enlightened side is always towards the sun, which shows 




How was the revolution of Mercury, on an axis, determined ? Does 
Venus revolve on an axis, and in what time V 



130 ELEMENTARY ASTRONOMY. 

that it shines not by its own light, but by reflecting the light 
from the sun ; and indeed, observations show that this is true 
of all the planets. For the magnitude, motion, inclination of 
orbit, &c. of Venus, see tables. 

THE EARTH 

Is the next planet in the system ; but it would be only for- 
mality to give any description of it in this connection. As a 
planet, it seems to be highly favored above its neighboring 
planets, by being furnished with an attendant, the moon ; and 
insignificant as this latter body is, compared to the whole solar 
system, it is the most important to the inhabitants of our earth. 
The two bodies, the earth and the moon, as seen from the sun, 
are very small : the former subtending an angle of about 17" 
in diameter, and the latter about 4", and their distance asunder 
never greater than between seven and eight minutes of a degree. 

We shall give a particular description of the moon, its orbit, 
motion, &c. &c. in a future chapter. 

MARS. 

The fourth planet from the sun is Mars ; its orbit is nearest 
the orbit of the earth, or it is the first superior planet. It is 
of a fiery red color, and very variable in its apparent magni- 
tude corresponding with its va- 
riable distance. About every 
other year, when it comes to 
the meridian near midnight, it 
is then most conspicuous ; and 
the next year it is scarcely no- 
ticed by the common observer. 
The figure in the margin 
represents the telescopic ap- 
pearance of Mars when its ap- 
parent magnitude is greatest, near its opposition to the sun. 

Does Venus shine by its own light? and if not, how is that fact known? 
What heavenly body is most important to the inhabitants of the earth, 
(the sun excepted)? What is the position of Mars in the solar system? 
Describe that planet. Why is it much more conspicuous sometimes than 
others? When most conspicuous, what is its position in respect to the sun? 




DESCRIPTION OF THE SOLAR SYSTEM. 131 

"The physical appearance of Mars is somewhat remarkable. 
His polar regions, when seen through a telescope, have a bril- 
liancy so much greater than the rest of his disc, that there can 
be little doubt that, as with the earth so with this planet, accu- 
mulations of ice or snow take place during the winters of those 
regions. In 1781 the south polar spot was extremely bright ; 
for a year it had not been exposed to the solar rays. The color 
of the planet most probably arises from a dense atmosphere 
which surrounds him, of the existence of which there is other 
proof depending on the appearance of stars as they approach 
him ; they grow dim and are sometimes wholly extinguished 
as their rays pass through that medium. ,, 

The next planet known to ancient astronomers, is Jupiter ; 
but its distance is so great beyond the orbit of Mars, that the 
void space between the two had often been considered as an 
imperfection, and it was a general impression among astrono- 
mers that a planet ought to occupy that vacant space. 

For complete symmetry in the solar system, a planet ought 
to exist at about 2.8 distance from the sun, calling the distance 
of the earth unity, and that planet two or three times the mag- 
nitude of the earth, — but certainly no such planet existed, for 
such an one could not possibly have escaped observation. 

Mere human reason had long decided that a planet ought to 
exist in this void space, and in this case, reason has triumphed. 
On the 1st of January, 1801, M. Piazzi, an astronomer of Pa- 
lermo, in Sicily, discovered a small planet, which he called 
Ceres, which was soon found to occupy this very vacant space. 
This set other astronomers on the alert, and three other small 
planets were discovered between January, 1801, and April, 
1807. The following table gives much information in a very 
small compass : 



Planets. 


Names of Dis- 
coverers. 


Residence of Discoverers. 


Date of Discovery. 


Ceres, 
Pallas, 
Juno, 
Vesta, 


M. Piazzi, 
Dr. Olbers, 
M. Harding, 
Dr. Olbers, 


Palermo, Sicily, 
Bremen, Germany, 
Lilienthal, near Bremen, 
Bremen, 


1st January, 1801. 

28th March, 1802. 

1st September, 1804. 

29th March, 1807. 



For complete symmetry, thereabouts in the solar system should a large 
planet exist? When was the first planet discovered in that space ? 



132 ELEMENTARY ASTRONOMY. 

These planets revolving at nearly the same mean distance 
from the sun, and performing their revolutions in times of near 
the same duration — and being very small, Dr. Olbers suggested 
that they might be but fragments of one large planet that burst 
asunder by its internal fires. 

This bold and original idea was received as visionary, and 
by some, with sneers, as all bold and original ideas always 
have been received at first, but time and reflection have grad- 
ually brought this theory into favor. 

If a planet has really burst, it is but reasonable to suppose 
that it separated into many fragments ; and, agreeably to this 
view of the subject, astronomers have been constantly on the 
alert for new planets, in the same regions of space ; and every 
discovery of the kind greatly increases the probability of the 
theory. 

On the 8th of December, 1845, Mr. Hencke, of Dresden, 
discovered a planet called Astrea, and the same observer dis- 
covered another in 1847, called Hebe. 

The success of Mr. Hencke induced others to like examina- 
tions in the heavens, and Mr. Hind, of London, in 1848, dis- 
covered two other planets, Iris and Flora. 

Since this time, seven other small planets have been dis- 
covered, Egeria, JEunomia, Irene, Metis, Parthenope, Hygeria, 
and Victoria. Thus, we have fifteen* miniature worlds, all 
located in that space where reason called for a planet ; and, is 
it unreasonable then to suppose that these fifteen, and perhaps 
others yet unseen, are but fragments of a planet ? all of them 
together would not make one planet larger than the earth. 

* This chapter "was written in 1854, since which time, and up to the 
present, some seventeen others have been added to the list. At this time, 
1857, thirty-one have been tabulated in the Nautical Almanac; but all of 
them put together would not make a very large planet, and they are of no 
interest to readers of this work. "We have tabulated some on the next page. 

On finding four planets in this region, what theory was advanced by 
Dr. Olbers ? Is it reasonable to suppose that all of these small bodies at 
about the same mean distance from the sun, could be originally distinct 
and independent planets ? 



DESCRIPTION OF THE SOLAR SYSTEM. 



133 



For further information, we give the following tabular facte, 
which will be verified, or modified and corrected, by subse- 
quent observations : 



Planets. 



Flora, 

Victoria, 

*Vesta, 

Iris, 

Metis, 

Hebe, 

Parthenope, 

Irene, 

Astrea, 

Egeria, 

*Juno, 

* Ceres, 

*Pallas, 

Eunomia, 

Hygeia, 

Psyche, 

Fortuna, 

Melpomene, 

Thetis, 

Lutetia, 

Calliope, 

Amphitrite, 



Mean dis- 
tance from 
the sun. 



Earth's dis. 1 

2.2014 
2.3348 
2.3627 
2.3858 
2.3868 
2.4256 
2.4483 
2.5805 
2.6173 
2.5829 
2.6679 
2.7653 
2.7715 
2.6483 
3.1512 
2.9771 
2.5342 
2.3292 
2.4718 
2.4353 
2.9054 
2.5521 



Mean time 
of Revolu- 
tion. 



Eccentricity 
of orbits. 



Days. 

1193.16 
1303.08 
1326.26 
1345.66 
1346.90 
1379.68 
1399.06 
1515.40 
1547.58 
1515.82 
1591.68 
1679.86 
1686.22 
1574.08 
2043.38 
1834.61 
1440.80 
1269.81 
1419.31 
1387.77 
1809.00 
1489.22 



Lon. of the 
Ascending 
node. 



0.15677 
0.21854 
0.08945 
0.23232 
0.12274 
0.20200 
0.09800 
0.16974 
0.18880 
0.08628 
0.25637 
0.07904 
0.23894 
0.18856 
0.10090 
0.13082 
0.17023 
0.21644 
0.12736 
0.16104 
0.10308 
0.06716 



110° 21' 
235° 40' 
103° 24' 
259° 44 

68° 28' 
138° 32' 
125° 0' 

86° 51' 
141° 28 

43° 18' 
170° 58' 

80° 49' 
172° 37' 
293° 54' 
287° 38' 
150° 36' 
211° 17' 
150° 0' 
125° 25' 

80° 34' 

66° 38' 
356° 27' 



Inclination 


of orbit. 


To Ecliptic. 


5° 


53' 


8° 


23' 


7° 


8' 


5° 


28' 


5° 


36' 


14° 


47' 


4° 


37' 


9° 


6' 


5° 


19' 


16° 


33' 


13° 


3' 


10° 


36' 


34° 


42' 


11° 


44' 


3° 


47' 


3° 


4' 


1° 


32' 


10° 


9' 


5° 


35' 


3° 


5' 


13° 


45' 


6° 


8' 



The hypothesis that the small planets, Ceres and Pallas, 
were originally one planet, and must, therefore, by the laws of 
motion and inertia, have two common points in the heavens, 
near which all of them must pass, led to the discovery of Juno 
and Vesta, by carefully observing in these two portions of the 
heavens for other fragments which might exist ; and as this 
theory came more and more into favor, observations were made 



* We made an effort to arrange these planets in the order of their 
distances from the sun, and we have done so, as far as Hygeia. The fol- 
lowing ones were subsequent discoveries. Some future day, when these 
elements will be better known, by more varied and extended observations, 
a re- arrangement can be made. 



134 ELEMENTARY ASTRONOMY. 

with greater and greater care, and the result has been, these 
recent interesting and singular discoveries. 

The apparent diameters of these planets are too small to be 
accurately measured ; and therefore we have only a very rough 
or conjectural knowledge of their diameters. 

All of these planets are invisible to the naked eye, except 
Vesta, which sometimes can be seen as a star of the 5th or 6th 
magnitude. 

The fact that these bodies have never caused any sensible 
perturbations in the motion of Mars, is a physical demonstra- 
tion that they must be very small, separately considered, and 
their aggregate influence must be nearly frittered away, in 
consequence of their dispersed positions. 

JUPITER. 

We now come to the most magnificent planet in the system 
— the well-known Jupiter — which is nearly 1300 times the 
magnitude of the earth. 

The disc of Jupiter is always observed to be crossed, in an 
eastern and western direction, by dark bands, as represented 
in the annexed figure. 







"What is said of the diameters and real magnitudes of these planets? 
Which planet is the most magnificent in the system ? 



DESCRIPTION OF THE SOLAK SYSTEM. 135 

M These belts are, however, by no means alike at all times ; 
they vary in breadth and in situation on the disc (though never 
in their general direction). They have even been seen broken 
up, and distributed over the whole face of the planet : but this 
phenomenon is extremely rare. Branches running out from 
them, and subdivisions, as represented in the figure, as well as 
evident dark spots, like strings of clouds, are by no means 
uncommon; and from these, attentively watched, it is con- 
cluded that this planet revolves in the surprisingly short period 
of 9h. 55m. 50s. (sid. time), on an axis perpendicular to the 
direction of the belts. Now, it is very remarkable, and forms 
a most satisfactory comment on the reasoning by which the 
spheroidal figure of the earth has been deduced from its diur- 
nal rotation, that the outline of Jupiter's disc is evidently not 
circular, but elliptic, being considerably flattened in the direc- 
tion of its axis of rotation. 

"The parallelism of "the belts to the equator, of Jupiter, 
their occasional variations, and the appearances of spots seen 
upon them, render it extremely probable that they subsist in 
the atmosphere of the planet, forming tracts of comparatively 
clear sky, determined by currents analogous to our tradewinds, 
but of a much more steady and decided character, as might 
indeed be expected from the immense velocity of its rotation. 
That it is the comparatively darker body of the planet which 
appears in the belts, is evident from this, — that they do not 
come up in all their strength to the edge of the disc, but fade 
away gradually before they reach it. 

" When Jupiter is viewed with a telescope, even of moderate 
power, it is seen accompanied by four small stars, nearly in a 
straight line parallel to the ecliptic. These always accompany 
the planet, and are called its Satellites. They are continually 

In what time does Jupiter revolve on its axis? Those dark belts on 
Jupiter, are they on the body of the planet, or are they probably clouds 
in its atmosphere ? Is Jupiter exactly spherical ? How many moons 
has Jupiter ? 



136 ELEMENTARY ASTRONOMY. 

changing their positions with respect to one another, and to the 
planet, being sometimes all to the right, and sometimes all to 
the left ; but more frequently some on each side. The greatest 
distances to which they recede from the planet, on each side, 
are different for the different satellites, and they are thus dis- 
tinguished : that being called the First satellite, which recedes 
to the least distance ; that the Second, which recedes to the 
next greater distance, and so on. The satellites of Jupiter 
were discovered by Galileo, in 1610. 

" Sometimes a satellite is observed to pass between the sun 
and Jupiter, and to cast a shadow which describes a chord 
across the disc. This produces an eclipse of the sun, to Jupi- 
ter, analogous to those which the moon produces on the earth. 
It follows that Jupiter and its satellites are opake bodies, which 
shine by reflecting the light of the sun. 

" Careful and repeated observations show that the motions 
of the satellites are from west to east, in orbits nearly circular, 
and making small angles with the 'plane of Jupiter's orbit. 
Observations on the eclipses of the satellites make known their 
synodic revolutions, from which their sidereal revolutions are 
easily deduced. From measurements of the greatest apparent 
distances of the satellites from the planet, their real distances 
are determined. 

" A comparison of the mean distances of the satellites, with 
their sidereal revolutions, proves that Kepler's third law, with 
respect to the planets, applies also to the satellites of Jupiter. 
The squares of their sidereal revolutions are as the cubes of 
their mean distances from the planet. 

" The planets Saturn and Uranus are also attended by satel- 
lites, and the same law has place with them. ,, 

By the eclipses of Jupiter's satellites, the progressive nature 

Do the revolutions of these moons correspond to Kepler's third law? Re- 
peat the law. What discovery was made in relation to light, by the aid 
of the eclipses of Jupiter's moons ? Explain this by a figure on the black 
board. 



DESCRIPTION OF THE SOLAR SYSTEM. 137 

of light was discovered ; which we illustrate in the following 
manner : 




Let S represent the sun, J Jupiter, E Earth, and m Jupiter's 
first satellite. By careful and accurate observations astrono- 
mers have decided that the mean revolution of this satellite 
round its primary, is performed in 42h. 28m. and 35s.; that is, 
the mean time from one eclipse to another. 

But when the earth is at E, and moving in a direction to- 
ward, or nearly toward, the planet as represented in the figure, 
the mean time between two consecutive eclipses is shortened 
about fifteen seconds ; and we can explain this on no other 
hypothesis than that the earth has advanced and met the suc- 
cessive progression of light. When the earth is in position as 
respects the sun and Jupiter, as represented in our figure at E", 
and moving from Jupiter, then the interval between two con- 
secutive eclipses of Jupiter's first satellite is prolonged or 
increased about fifteen seconds. 

But during the interval of one revolution of Jupiter's first 
satellite, the earth moves in its orbit about 2880000 miles ; 
this, divided by 15, gives 192000 miles for the motion of light 
in one second of time ; and this velocity will carry light from 
the sun to the earth in about eight and one-fourth minutes. 

As an eclipse of one of Jupiter's satellites may be seen from 
all places where the planet is then visible, two observers view- 
ing it will have a signal for the same moment, at their respective 

How do astronomers find the difference of longitude between two places 
by means of the eclipses of Jupiter's satellites V 
1? 



138 ELEMENTARY ASTRONOMY. 

places ; and their difference in local time, will give their dif- 
ference in longitude. For example, if one observer saw one 
of these eclipses at lOh. in the evening, and another at 8h. 
30m., the difference of longitude between the observers would 
be lh. 30m. in time, or 22° 30' of arc. 

The absolute time that the eclipse takes place, is the same 
to all observers ; and he who has the latest local time is the 
most eastward. 

These eclipses cannot be observed at sea, by reason of the 
motion of the vessel. The telescope cannot be held sufficiently 
steady. 

SATURN. 

The next planet in order of remoteness from the sun, is 
Saturn, the most wonderful object in the solar system. Though 
less than Jupiter, it is about 79000 miles in diameter, and 1000 
times greater than our earth. 

" This stupendous globe, besides being attended by no less 
than seven satellites, or moons, is surrounded with two broad, 
flat, extremely thin rings, concentric with the planet and with 
each other ; both lying in one plane, and separated by a very 
narrow interval from each other throughout their whole cir- 
cumference, as they are from the planet by a much wider. 
The dimensions of this extraordinary appendage are as follows : 

Miles. 
Exterior diameter of exterior ring, = 176418 

Interior ditto, = 155272 

Exterior diameter of interior ring, = 151690 

Interior ditto, = 117339 

Equatorial diameter of the body, = 79160 

Interval between the planet and interior ring, . . = 19090 

Interior of the rings, = 1791 

Thickness of the rings not exceeding = 100 

Can these eclipses be used at sea? Why not? "What is the next planet 
in the system ? What is the magnitude of Saturn ? What is there re- 
markable about the planet ? Ho-w many moons has it ? 



DESCRIPTION OF THE SOLAR SYSTEM. 139 

" The figure represents Saturn surrounded by its rings, and 
having its body striped with dark belts, somewhat similar, but 




broader and less strongly marked than those of Jupiter, and 
owing, doubtless, to a similar cause. That the ring is a solid 
opake substance, is shown by its throwing its shadow on the 
body of the planet, on the side nearest the sun, and on the 
other side receiving that of the body, as shown in the figure. 
From the parallelism of the belts with the plane of the ring, it 
may be conjectured, that the axis of rotation of the planet is 
perpendicular to that plane ; and this conjecture is confirmed 
by the occasional appearance of extensive dusky spots on its 
surface, which when watched, like the spots on Mars or Jupiter, 
indicate a rotation in lOh. 29m. 17s. about an axis so situated. 
" It will naturally be asked how so stupendous an arch, if 
composed of solid and ponderous materials, can be sustained 
without collapsing and falling in upon the planet ? The answer 
to this is to be found in a swift rotation of the ring, in its own 
plane, which observation has detected, owing to some portions 
of the ring being a little less bright than others, and assigned 
its period at lOh. 29m. 17s., which, from what we know of its 
dimensions, and of the force of gravity in the Saturnian sys- 
tem, is very nearly the periodic time of a satellite revolving at 
the same distance as the middle of its breadth. It is the cen- 
trifugal force, then, arising from this rotation, which sustains 
it ; and, although no observation nice enough to exhibit a 

Which is most probable, that the rings are solid, or consist of vapor? 
Do the rings revolve ? In what length of time ? 



4 

140 ELEMENTARY ASTRONOMY. 

difference of periods between the outer and inner rings, have 
hitherto been made, it is more than probable that such a dif- 
ference does exist, so as to place each, independently of the other, 
in a similar state of equilibrium. 

" Although the rings are, as we have said, very nearly con- 
centric with the body of Saturn, yet recent micrometrical 
measurements, of extreme delicacy, have demonstrated that 
the coincidence is not mathematically exact, but that the 
center of gravity of the rings oscillates round that of the body, 
describing a very minute orbit, probably under laws of much 
complexity. Trifling as this remark may appear, it is of the 
utmost importance to the stability of the system of the rings. 
Supposing them mathematically perfect in their circular form, 
and exactly concentric with the planet, it is demonstrable that 
they would form (in spite of their centrifugal force) a system 
in a state of unstable equilibrium, which the slightest external 
power would subvert — not by causing a rupture in the sub- 
stance of the rings — but by precipitating them, unbroken, on 
the surface of the planet. For the attraction of such a ring or 
rings on a point or sphere eccentrically situate within them, is 
not the same in all directions, but tends to draw the point or 
sphere toward the nearest part of the ring, or away from the 
center. Hence, supposing the body to become, from any cause, 
ever so little eccentric to the ring, the tendency of their mu- 
tual gravity is, not to correct, but to increase this eccentricity, 
and to bring the nearest parts of them together." 

URANUS. 

This planet, the next beyond Saturn, was discovered by Sir 
W. F. Herschel, in 1781, and, for a time, was called Herschel, 
in honor of its discoverer; but, according to custom, the name 
of a heathen deity has been substituted, and the planet is now 
called Uranus — the father of Saturn. 

Is it probable that the rings revolve around Saturn, as moons in orbits 
slightly eccentric ? Is this necessary to preserve the existence of the rings 
unbroken ? What is the next planet in the system ? When, and by whom 
was it discovered ? 



DESCRIPTION OF THE SOLAR SYSTEM. 141 

This planet is rarely to be seen, without a telescope. In a 
clear night, and in the absence of the moon, when in a favor- 
able position above the horizon, it may be seen as a star of 
about the sixth magnitude. Its real diameter is about 35000 
miles, and about 80 times the magnitude of the earth. 

The existence of this planet was suggested by some of the 
perturbations of Saturn ; which could not be accounted for by 
the action of the then known planets ; but it does not appear 
that any computations were made, as a guide to the place 
where the unknown disturbing body ought to exist ; and, as far 
as we know, the discovery by Herschel w r as merely accidental. 

Not so in respect to the discovery of the most remote planet 
now known in the solar system — the planet 

NEPTUNE. 

This planet was discovered in the latter part of September, 
1846, by a French astronomer, Leverrier; and also a Mr. Adams, 
of Cambridge, England, who has put in his claim as discoverer. 
The truth is, that the attention of the astronomers of Europe 
had been called to some extraordinary perturbations of Uranus; 
which could not be accounted for without supposing an attract- 
ing body to be situated in space, beyond the orbit of Uranus ; 
and so distinct and clear were these irregularities, that both 
geometers, Leverrier and Adams, fixed on the same region of 
the heavens, for the then position of their hypothetical planet ; 
and by diligent search, the planet was actually discovered 
about the same time, in both France and England. All that is 
known of this planet is comprised in the following table : 

Epoch 1852, Sept. 3d, mean time at Berlin. 

Mean lono-itude, - - - 341° 1' 55"} ^ 

° ' / From mean 

Longitude of the Perihelion, 47° 16' 36"> Equinox. 

Longitude of Ascending Node, 130° 8' 50") 

Inclination of the orbit, - 1° 46' 59' 

What observed facts suggested the existence of Uranus ? Was the dis- 
covery the result of such an hypothesis ? What other planet was dis- 
covered by similar facts, and a similar theory ? When and by whom was 
that planet, discovered ? 



142 ELEMENTARY ASTRONOMY. 

Eccentricity of the orbit, - - 0.008718 
Mean daily sidereal motion, - 2 1 ".5545 

Mean time of revolution, 60126.65 days, or 165 yrs. nearly. 
Mean distance from the sun, 30.048, (the earth's distance 
being unity.) Future observations will undoubtedly modify 
and correct these results. 

We shall close this chapter with the following extract from 
Herschel's Astronomy, "which will convey to the minds of our 
readers a general impression of the relative magnitudes and 
distances of the parts of our system. Choose any well-leveled 
field or bowling green. On it place a globe, two feet in diam- 
eter ; this will represent the sun ; Mercury will be represented 
by a grain of mustard seed, on the circumference of a circle 
164 feet in diameter for its orbit ; Venus a pea, on a circle 284 
feet in diameter ; the earth also a pea, on a circle 430 feet ; 
Mars a rather large pin's head, on a circle of 654 feet ; Juno, 
Ceres, Yesta, and Pallas, grains of sand, in orbits of from 1000 
to 1200 feet; Jupiter a moderate-sized orange, in a circle 
nearly half a mile across ; Saturn a small orange, on a circle 
of four-fifths of a mile ; and Uranus a full-sized cherry, or 
small plum, upon the circumference of a circle more than a 
mile and a half in diameter. As to getting correct notions on 
this subject by drawing circles on paper, or still worse, from 
those very childish toys called orreries, it is out of the ques- 
tion. To imitate the motions of the planets in the above men- 
tioned orbits, Mercury must describe its own diameter in 41 
seconds; Venus, in 4m. 14s. ; the earth, in 7 minutes ; Mars, 
in 4 m. 48s. ; Jupiter, in 2h. 56m.; Saturn, in 3h. 13m.; and 
Uranus, in 2h. 16m." 

From this description it will be seen that the true reason 
why the solar system cannot be accurately represented on 
paper, is this : That if we give the earth any sensible magni- 
tude, there will not be space enough on any paper to represent 
the sun, or to extend to the planets. 

"What does Herschel say about representing the solar system on paper ? 
What terra does he apply to orreries ? Why ran vre not make a proper 
map of the solar system ? 



SECTION III 



CHAPTER I. 

THE MOON", ITS PERIODICAL REVOLUTIONS, 
AND APPEARANCES. 

Next to the sun, the moon is the most interesting and im- 
portant heavenly body, to the inhabitants of the earth, and we 
made that a reason for omitting an exposition of its motion, 
path, and other phenomena, until the student acquired a little 
astronomical discipline. In Section II, chapter I, we have 
explained parallax in general, and the moon's parallax in par- 
ticular, and found it to vary from 53' 50" to 61' 29", the amount 
when the moon is at its mean distance from the earth, being 
57' 3", corresponding to a distance of 60.26 semi-diameters 
from the earth. 

The position of the moon, in right ascension and declination, 
can be determined almost daily, at any observatory, when it 
passes the meridian ; and before observatories were established, 
the more rude observations of its approximate positions among 
the stars, from time to time, were sufficient to establish its 
periods with tolerable accuracy. Observations long continued, 
have established the fact that the average, or mean time, of the 
revolution of the moon from the longitude of any fixed star to 
the longitude of the same star again, is 27 days, 7 hours, 43 
minutes, 1 1 seconds ; this is called its sidereal revolution. Its 
revolution in respect to the equinoxes is 7 seconds less, because 
the equinox itself runs back, or westward among the stars. 
This revolution is called the tropical revolution. 

What is the moon's mean parallax and mean distance ? By "what kind 
of observations have the moon's periods been established ? What? is the 
mean revolution of the moon ? 



144 ELEMENTARY ASTRONOMY. 

The mean daily motion of the moon from west to east is 13° 
10' 35". The mean daily motion of the sun, in the same direc- 
tion is 0° 59' 08", hence the mean daily motion of the moon 
exceeds that of the sun by 12° 11' 27", which will give a revo- 
lution in 29 days 12 hours 44 minutes and 3 seconds, which 
is called the synodic revolution. This is the average time 
from new moon to new moon again, and from full moon to full 
moon again. 

This interval is also called a lunation. Some lunations do 
not exceed 29 days and 7 hours, and others come near 29 days 
and 18 hours. 

The •minimum lunations take place when the moon changes a 
day or two after the moon has passed its perigee, and the maxi- 
mum lunations take place when the moon changes a day or two 
after the moon has passed its apogee. If all lunations were 
alike in length of time, any one who can work problems in 
proportion, could compute the times of new and full moon. 
As it is, the computations are quite troublesome, as every dis- 
turbing cause of motion has to be separately considered and 
allowed for. 

To illustrate one of the principal causes 
of the inequality of lunations, we give the 
figure in the margin. Let E be the posi- 
tion of the earth, and CADB the moon's 
orbit, the moon moving in the direction 
from A to D and from D to B, and so on, 
round the ellipse. 

Let S'be the direction of the sun ; then 
when the moon is near i?,it is in conjunction 
with the sun. In 27d. 7h. 43m., or there- 
abouts, the moon will be round to the same point B again, but 
during that time the sun has apparently moved from S'lo S, 
about 27°, and the moon, to come again in range with the sun, 

What is the mean daily motion of the moon, in longitude ? "What is 
the time from new moon to new moon again ? Why is this interval not 
always the same ? When is the interval the longest ? When the shortest ? 




LUNAR MOTIONS. 145 

must pass over about 27°; but now, the moon being at its 
greatest distance from the earth, its motion is much slower 
than its mean motion, and therefore the time required to de- 
scribe this excess arc, will be greater than the mean time, and 
thus cause a long lunation. 

When the new moon takes place at B, the full moon will take 
place at A, and along in that part of the moon's orbit, the 
excess arc will be passed over by the moon in less than the 
average time, and thus cause the interval from full moon to 
full moon again, to be less than the average time, or a short 
lunation. 

By observing the moon's altitude when it comes on to the 
meridian, from time to time, it was early ascertained, that its 
pathway through the heavens among the stars, was not the 
same as that of the sun, but that the plane of its orbit was 
inclined to the plane of the ecliptic by an angle varying from 
4 Q 58' to 5° 18', the mean inclination being 5° 8'; the variation 
being caused by the disturbing action of the sun's attraction, 
that being different under different circumstances. The points 
where the moon's path crosses the ecliptic (the sun's path) are 
called the moon's nodes; the one where the moon passes from 
the south side of the ecliptic to the north side, is called the 
ascending node y and the one on the opposite side of the sphere 
where the moon crosses from the north side of the ecliptic to 
the south side, is called the descending node. The nodes are not 
stationary in the heavens — they move backward on the ecliptic 
on an average of 19° 19' 44" in a year, which will cause a com- 
plete revolution of the nodes in 18 years 228 days and 9 hours; 

J 

19° 19' 44"/ 
This period is nearer 19 than 18 years, and it is a period in 
which the path of the moon through the heavens is very nearly 

By what observation was the inclination of the moon's orbit to the eclip- 
tic determined ? What is that inclination ? What are these points called, 
when the moon crosses the ecliptic ? Arc these points stationary ? Id 
what time, and in what direction do they make a revolution? 
13 



146 ELEMENTARY ASTRONOMY. 

the same as it was 19 years before, and it is called the lunar 
cycle or golden number.* This period has a governing influence 
over solar and lunar eclipses, but we reserve that subject for 
the next chapter. 

When the sun is in, or near the moon's nodes, its attraction 
on the moon has no tendency to draw the moon out of the plane 
of its orbit, and at those times the natural inclination of the 
lunar orbit to the ecliptic is about 5° 18'. When the sun is 
90° from the moon's node, then the inclination of the lunar 
orbit to the ecliptic is often not more than 5°, because the ten- 
dency of the sun's attraction is then to draw the moon towards 
the ecliptic, and this same tendency actually causes the moon 
to run into the ecliptic sooner than it otherwise would, thus 
producing a retrograde motion of the nodes themselves. 

The points in the heavens where the moon arrives at its 
apogee and perigee, are generally opposite to each other, but 
rarely exactly so, — nor are these points stationary in the 
heavens — but make a direct revolution in 3231. 1 V 5 - days, 
nearly 9 years, — but the true motion is very variable, some- 
times backward, sometimes forward, and sometimes stationary, 
but the forward or direct motion towards the east prevails, 
making a revolution in the time just noted. 

The lunar apogee is much influenced by the position of the 
sun ; it is dragged after the sun (so to speak), when the sun is 
a little in advance of it, and retarded in its motion, and even 
retrograde in its motion, when the sun is a little west of it. In 
short, the lunar orbit is not an ellipse, but resembles that figure 
more nearly than any other, and it is continually varying in its 
general eccentricity. 

*The Athenians, 433 before Christ, inscribed this number in letters of 
gold on the walls of the temple of Minerva. Hence it is denominated the 
Goldex Number. 

What is the golden number ? "What makes the period ? Why so called? 
What causes the retrocession of the nodes ? Is the longer axis of the 
moon's orbit stationary in the heavens ? In what direction and in what 
time do the apogee and perigee points revolve ? 



LUNAR MOTIONS. 147 

The revolution of the apogee is called the anomalactic period. 

The fact that the same face of the moon is always towards 
the earth, shows that it turns on an axis in the same time it 
revolves round the earth, otherwise all sides of it would in time 
be presented to our view. 

The mean motion on its axis, and the mean motion or revo- 
lution round the earth, is exactly the same, — but the motion 
on its axis is uniform, and the motion in its orbit is variable, 
and this gives the face of the moon an apparent vascillating 
motion, which is called the moon's Vibration. 

There is a libration in longitude caused by the moon's unequal 
motion in longitude, and a libration in latitude caused by the 
varying inclination of its orbit with the ecliptic. 

" The moon, like the planets, is an opake body, and shines 
entirely by the light received from the sun, a portion of which 
is reflected to the earth. As the sun can only enlighten one- 
half of a spherical surface at once, it follows that according to 
the situation of an observer, with respect to the illuminated 
part of the moon, he will see more or less of the light reflected 
from her surface. At the conjunction, or time of new moon, 
the moon is between the earth and the sun, and consequently 
that side of the moon which is never seen from the earth, is 
enlightened by the sun ; and that side which is constantly 
turned towards the earth is wholly in darkness. Now, as the 
mean motion of the moon in her orbit exceeds the apparent 
motion of the sun by about 12° 11' in a day, it follows that, 
about four days after the new moon, she will be seen in the 
evening a little to the east of the sun, after he has descended 
below the western part of the horizon. A spectator will see 
the convex part of the moon towards the west, and the horns 
or cusps towards the east : or if the observer live in north 
latitude, as he looks at the moon the horns will appear to the 
left hand ; for if the line joining the cusps of the moon be 

What truth is revealed by the fact that the same face of the raoou is al- 
ways towards the earth? What is meant by libration, and from what does 
it arise ? How do we know that the moon docs not shine by its own light? 



148 • ELEMENTARY ASTRONOMY. 

bisected by a perpendicular passing through the enlightened 
part of the moon, that perpendicular will point directly to the 
sun. As the moon continues her motion eastward, a greater 
portion of her surface towards the earth becomes enlightened ; 
and when she is 90 degrees eastward of the sun, which will 
happen about 7} days from the time of new moon, she will 
come to the meridian about six o'clock in the evening, having 
the appearance of a bright semi-circle. Advancing still to the 
eastward, she becomes more enlightened towards the earth, 
and at the end of about 14| days, she will come to the meri- 
dian at midnight, being diametrically opposite to the sun ; and 
consequently she appears a complete circle, and it is said to be 
full moon. The earth is now between the sun and the moon, 
and that half of her surface, which is constantly turned towards 
the earth, is wholly illuminated by the direct rays of the sun ; 
whilst that half of her surface, which is never seen from the 
earth, is involved in darkness. The moon continuing her pro- 
gress eastward, she becomes deficient on her western edge, and 
about 7^- days from the full moon she is again within 90 degrees 
of the sun, and appears a semi-circle with the convex side 
turned towards the sun: moving on still eastward, the deficiency 
on her western edge becomes greater, and she appears a cres- 
cent, with the convex side turned towards the east, and her 
cusps or horns turned towards the west: and about 14-^- days 
from the full moon she has again overtaken the sun, this period 
being performed in 29 days 12 hours 44 minutes 3 seconds, at 
a mean rate, as has been mentioned before. Hence, from the 
new moon to the full moon, the phases are horned, half-moon, 
and gibbous; and as the convex or well-defined side of the moon 
is always turned towards the sun, the horns or irregular side 
will appear to the east, or towards the left hand of a spectator 
in north latitude. From the full moon to the change, the phases 

When the moon is full, what is its position in respect to the sun ? "When 
the moon is at the first quarter, what is its position in respect to the sun? 
When at the last quarter, what is its position, and about -what time would 
it come to the meridian ? 



LUNAR APPEARANCES. 



149 



are gibbous, half-moon, and horned; the convex or well-defined 
side of her face will appear to the east, and her horns or irregu- 
lar side towards the west, or to the right hand of a spectator. 

" As the full moons always happen when the moon is directly 
opposite to the sun, all the full moons, in our winter, happen 
when the moon is on the north side of the equinoctial. The 
moon, while she passes from Aries to Libra, will be visible at 
the north pole, and invisible during her progress from Libra to 
Aries ; consequently, at the north pole, there is a fortnight's 
moonlight and a fortnight's darkness by turns. The same 
phenomena will happen at the south pole during the sun's ab- 
sence in our summer." 

The surface of the moon is greatly diversified with inequali- 




"What is said of the full moons in winter ? Do the full moons of summer 
run high, or low? 



150 ELEMENTARY ASTRONOMY. 

ties, which, through a telescope, have all the appearances of 
hills, mountains, and valleys. Many attempts have been made, 
with considerable success, to delineate the face of the moon on 
paper, as it appears through a telescope, and the figure on the 
preceding page is a copy of one of them. 

Dr. Herschel informs us that, on the 19th of April, 1787, 
he discovered three volcanoes in the dark pan of the moon, 
two of them apparently extinct, the third exhibited an actual 
eruption "of fire, or luminous matter. On the subsequent night 
it appeared to burn with greater violence, and might be computed 
to be about three miles in diameter. The eruption resembled 
a piece of burning charcoal, covered by a thin coat of white 
ashes; all the adjacent parts of the volcanic mountain were 
faintly illuminated by the eruption, and were gradually more 
obscure at a greater distance from the crater. That the surface 
of the moon is indented with mountains and caverns, is evident 
from the irregularity of that part of her surface which is turned 
from the sun : for, if there were no parts of the moon higher 
than the rest, the light and dark parts of her disc at the time 
of her quadratures, would be terminated by a perfectly straight 
line ; and at all other times the termination would be an ellip- 
tical line, convex towards the enlighted part of the moon, in the 
first and fourth quarters, and concave in the second and third: 
but instead of these lines beino; reo-ular, and well defined, when 
the moon is viewed through a telescope, they appear notched, 
and broken in innumerable places. It is rather singular that 
the edge of the moon, which is always turned towards the sun, 
is regular and well defined, and at the time of full moon no 
notches or indented parts are seen on her surface. In all situ- 
ations of the moon, the elevated parts are constantly found to 
cast a triaugular shadow with its vertex turned from the sun ; 
and, on the contrary, the cavities are always dark on the side 
next the sun, and illuminated on the opposite side : these ap- 
pearances are exactly conformable to what we observe of hills 

How long are the winter full moons visible from the north pole ? What 
full moons are visible more than 24 hours, as seen from the north pole ? 



LUNAR ATMOSPHERE. 151 

and valleys on the earth : and even in the dark part of the moon's 
disc, near the borders of the lucid surface, some minute specks 
have been seen, apparently enlightened by the sun's rays : 
these shining spots are supposed to be the summits of high 
mountains, which are illuminated by the sun, while the ad- 
jacent valleys nearer the enlightened part of the moon are 
entirely dark. 

Whether the moon has an atmosphere or not, is a question 
that has long been controverted by various astronomers ; some 
endeavor to prove that the moon has neither an atmosphere, 
seas, nor lakes ; while others contend that she has all these in 
common with our earth, though her atmosphere is not so dense 
as ours." 

Whenever our own atmosphere is clear and transparent, 
every appearance of hill, and valley — all the varieties of light, 
and shade — indeed, all the spots on the moon are equally well 
defined and distinct, and this could not be, were the moon sur- 
rounded with an atmosphere capable of holding vapors, and 
clouds, like the atmosphere of our earth. Therefore, most 
astronomers conclude that such an atmosphere does not there 
exist. 

On the other hand, we must not forget — that volcanoes have 
been observed on the moon — and we can have no distinct idea 
of combustion, without an atmosphere or a gas, to support it. 
An atmosphere might exist, having no affinity for vapors, one 
that would be transparent, and, in that case we could always 
see through it, as though it did not exist; and if the moon has 
an atmosphere, it must be one of that kind. 

But of all this, nothing is positively known. 

What is the appearance of the edge of the moon between the illuminated 
and unilluminated parts? What does this appearance surely indicate? 
Why have astronomers contended that the moon has no atmosphere ? Are 
you sure the moon has no atmosphere ? What kind of an atmosphere may 
it have ? 



152 ELEMENTARY ASTRONOMY. 

CHAPTER II. 

ECLIPSES. 

The path of the sun through the heavens is the same every 
year. It is the ecliptic, so called, because all eclipses of the 
sun, and moon, take place when the moon is in or near this line. 

If the moon's path round the sphere were the same as the 
sun's, that is, if the moon were all the while in the ecliptic, 
there would be an eclipse of the sun at every new moon, and 
an eclipse of the moon at every full moon. The moon's orbit 
or path, as we have seen in the preceding chapter, intersects 
the ecliptic or sun's path at an angle of 5° 8'; the points of in- 
tersection are called the moon's nodes ; and when the sun is in 
that part of the ecliptic near the moon's nodes, the moon cannot 
pass its conjunction with the sun without falling in range be- 
tween some part of the ecliptic, and some part of the earth, and 
that produces an eclipse of the sun. The two nodes are 
opposite to each other, and when the sun is near one node, the 
full moon will take place when the moon is near the other node ; 
and the sun, earth, and moon will be near one right line — the 
earth between the sun and moon — and then the moon must fall 
into some portion of the earth's shadow, and this produces an 
eclipse of the moon. 

If the moon's nodes were always at the same points on the 
ecliptic, eclipses would take place in the same months every year, 
but the nodes moving backward about 19° 19' each year, the 
eclipses, on an average, come about 19 days earlier each suc- 
ceeding year. Because the two nodes are opposite to each 

Why is the path of the sun among the stars called the ecliptic ? If the 
sun and moon passed round the earth in the same circle or path, how ofien 
would eclipses occur? At what angle does the moon's path intersect the 
ecliptic ? Where must the sun be on the ecliptic at the time eclipses occur? 
If the moon's nodes were stationary, would eclipses then occur at the same 
seasons of the \ r ear continually? 



ECLIPTIC LIMITS, 153 

other, eclipses must happen about six months asunder. For 
instance, if an eclipse occurs in the month of March, in any 
year, there will certainly be one in September, or on some of 
the last days of August, at the new or full moon. If an eclipse 
occurs in June, there will certainly be another in December. 
If one occurs in May there will be another in November, and 
so on continually, the average being a few days less than six 
months, and from year to year, the average time being at in- 
tervals of about 346 days. 

Whenever the moon changes within 17° of either of the 
moon's nodes, there must be an eclipse of the sun. That is, 
the sun must then be within 17° of one of the nodes, because 
at the time of change, the longitude of both sun and moon is 
then the same. 

Whenever the moon fulls, when the sun is within 12° of 
either node, there must be an eclipse of the moon. 

Hence, the number of eclipses of the sun which take place 
in any long interval of time, (say 19 years) must be to the 
number of eclipses of the moon as 17 to 12. But, an eclipse 
of the sun is visible from only a very small portion of the earth 
at any one time, while an eclipse of the moon is visible from a 
whole hemisphere ; hence there are more visible eclipses of the 
moon than of the sun, as seen from any one place. 

The least number of eclipses that can take place in any one 
year is two, the greatest number seven, the average number is 
four. 

When but two eclipses occur in a year, they are both of the 
sun, and are central as seen from some portion of the earth 
near the plane of the ecliptic. That is, a central eclipse would 
be seen from some latitude near the sun's declination. For 
example : if in a certain year there were but two eclipses, both 

"Why do eclipses occur at opposite months of the year? Give the limits 
within which the sun must be at the time of the lunar changes, to produce 
eclipses? Give the ratio between the number of eclipses of the sun and 
moon that take place in any long interval ? State the least and greatest 
number of eclipses that can fake place in any one year. 



154 



ELEMENTARY ASTRONOMY. 




would bo of the sun, and suppose 
one of them should take place in 
June, the other would take place 
in December, and the one which 
took place in June would be cen- 
tral as seen from some latitude 
not far from 20° north, and the one 
in December would be central as 
seen from some latitude not far 
from 20° south. Eclipses of the 
sun which take place when the 
sun is 10 or more degrees from 
the node, are partial eclipses, visi- 
ble from places not far from the 
poles of the earth. 

To show more clearly that the 
sun and moon must come in con- 
junction near the moon's node, 
we give the figure in the margin. 

The right line through the cen- 
ter represents the equator, the 
curved line ^ r ' @ Lqj the ecliptic, 
and the other curved line repre- 
sents the moon's path crossing the 
ecliptic at £J and $>. The sun 
and moon are represented in con- 
junction a little beyond the sign 
@, but the two paths are here so far 
asunder, that the sun and moon 
cannot come in range with each 
other and produce an eclipse. It 
is obviously not so, on the paths 
near their intersections, that is, 
near the nodes. 

As here represented the as- 
cending node is in longtitude 
about 210°, and the descending 



ECLIPSES. 155 

node is in longitude about 30°, and this was the position of the 
nodes in the year 1846, and the sun is at these points of the 
ecliptic in April and October, and therefore the eclipses in that 
year must have been and really were in those months. 

To make a general and rough computation of the times that 
eclipses will occur, all we have to do is to get the position of 
one of the moon's nodes, by observation or otherwise, and 
then trace it back at the rate of 19° 19' for 365 days, or at the 
rate of 3'. 18 per day. 

On the 1st of January, 1850, the mean longitude of the 
moon's ascending node was 146° 7', the opposite node was 
therefore in longitude 326°. The sun attains the longitude of 
326° on or about the 15th day of February in each year, and 
the longitude of 146° on or about the 19th of August. There- 
fore the new and full moons that took place within twelve days 
of these times, must and did produce eclipses. 

Diminishing 146° 7' at the rate of 19° 19' for each 365 days, 
brought the moon's ascending node to 68° 47'. 8 on the 1st of 
January, 1854, and to 61° 23' on the 21st of May, 1854. 

The sun attains this longitude on the 22d of May, and on 
the 26th of May the moon changed. There must then have been 
an eclipse. The sun and moon at that time were about 4° past 
the moon's ascending node, just sufficient to cast the moon's 
shadow into the northern hemisphere, making a central eclipse 
at noon, in latitude 45° 33' north, in longitude 134° 45' west. 

The following figure may assist some learners to form a dis- 
tinct and general idea of eclipses. 




How far does the node run back in 365 days ? How much in one day ? 
If I give you the longitude of the node, can you tell rae at what times of 
the year eclipses will occur ? 



156 ELEMENTARY ASTRONOMY. 

When an observer is in the moon's shadow, the dark body 
of the moon appears to him on the face of the sun. When an 
observer on the earth is in a certain space adjoining the 
shadow, as at e and /, a part of the sun is obscured by a part 
of the moon. When the moon is in the earth's shadow, it 
cannot shine because the direct rays of the sun are intercepted 
by the earth, and the moon is said to be in an eclipse. Never- 
theless when the moon is near the center of the earth's shadow, 
a sufficient amount of light is refracted through the earth's 
atmosphere to render the moon darkly visible. 

When the moon is eclipsed to the inhabitants of the earth, 
the sun must be eclipsed to an observer on the moon. An ob- 
server on the moon will see the sun partially eclipsed, when 
the moon falls into the partial shadow marked P P. Although 
this figure answers our purpose to a certain extent, it also illus- 
trates and verifies the remarks made about figures on page 142. 
The distance from the center of the earth to the moon's orbit, 
is 30 diameters of the earth, but in the figure it is not three 
diameters. The distance to the sun is 400 times the distance 
to the moon, but in the figure it is not five times that distance. 
When the earth is made of any apparent magnitude, there is 
not space enough on any paper for a true representation of any 
of these things. 

In reality, the moon's shadow comes to a point at about the 
distance of the earth from the moon, sometimes before it ex- 
tends to the earth, and then we have an annidar y and not a 
total eclipse. 

When the moon is near her perigee, her shadow will extend 
beyond the earth; when near her apogee, it will not extend to the 
earth. 

As we have before seen, the mean motion of the moon 
exceeds that of the sun by such an amount as to bring the two 

Can the moon be seen when in a total eclipse ? Is the figure on page 
155 a true representation of the distances of the sun and moon ? and if not, 
why was it not made so ? Is the moon's shadow always of the same 
length ? and if not, what causes its ■*■ nation ? 



ECLIPSES. 157 

bodies in conjunction or opposition at the average interval of 
29d. 12h. 44m. 3s., and the retrograde motion of the node is 
such as to bring the sun to the same node at intervals of 346d. 
14h. 52m. 16s. 

Now let us suppose the sun, moon, and node are together at 
any point of time, and in a certain unknown interval of time, 
which we represent by P, they will be together again. In this 
time P, we will suppose the moon to have accomplished m 
lunations, and the sun to have returned to the same node n 
times. 

These suppositions give the following equations : 

(29c7. 12A. Um.)m=P. (1) 

And (346d. Uh. 52m.)n=P. (2) 

Neglecting the seconds and reducing to minutes, we have 
42524m=P. (3) 

499132w=P. (4) 

Dividing (3) by (4), and reducing the numerator and de- 
nominator in the first member, gives us 
10631w =1 
124783"?T~ 

^ 10631 n 
Or = — 

124783 m 

As this fraction is irreducible, and as mand n must be whole 
numbers to answer the assumed conditions, therefore the smallest 
whole number for m is 124783, and for n 10631. 

That is, we see by equations (1) and (2), that to bring the 
sun, moon, and node a second time into conjunction, requires 
124783 lunations, or 10631 returns of the sun to the node, 
which is 10088 years, and about 197 days. 

We say about, because we neglected seconds in the periods 
of revolution, and because the mean motions will change in 
some slight degree in a period of so long a duration. 

What number of lunations are required for the suu, raoon, and node, to 
come in the same position a second time ? Even then, will the coincidences 
be exact? 



158 ELEMENTARY ASTRONOMY. 

This period, however, contemplates an exact return to the 
same positions of the sun, moon, and node, so that a line drawn 
from the center of the sun, through the center of the moon, will 
strike the earth at the same distance from the plane of the 
ecliptic ; but to produce an eclipse, it is not necessary that an 
exact return to former positions should be attained ; a greater or 
less approximation to former circumstances will produce a 
greater or less approximation to a former eclipse ; but exact 
coincidences, in all particulars, can never take place, however 
long the period. 

To determine the time when a return of eclipses may happen, 
(if we reckon from the most favorable positions), that is, com- 
mence with the supposition that the sun, moon, and node are 
together, it is sufficient to find the first approximate values of 

the fraction . 

124783 

If we find the successive approximate fractions, by the rule 
of continued fractions in arithmetic, we shall have the succes- 
sive periods of eclipses which will happen about the same 
node. 

The approximate fractions are 

JL_ JU -3- JL. JUL JLO_ 

11 12 35 4T 223 1831* 

These fractions show that at 1 1 lunations from the time an 
eclipse occurs, we may look for another; but if not at 11, it 
must be at 12, and it may be at both 1 1 and 12 lunations. 

At 5 and 6 lunations we shall find eclipses at the other node. 
To be more certain when an eclipse will occur, we take 35 
lunations from a preceding eclipse, which, is 1033 days and 14 
hours nearly. There was a total eclipse of the moon, 1851, 
July 12th, 19 hours. Add to this 1033 days 14 hours, will 
bring up to May 12th, 1854, the time of another lunar eclipse. 

If an eclipse occurs within 10° of the node, it is certain that 
an eclipse will again happen at the lapse of 47 lunations. 

The period, however, which is most known and most remark - 

What do the numerators of the series of fractions indicate on page 158? 
"What do the denominators Indicate? Lunations between what events ? 



ECLIPSES. 159 

able appears in the next fraction, which shows that 223 luna- 
tions have a very close approximate value to 19 revolutions of 
the sun to the node. 

223 lunations equal - 6585.32 days. 

19 returns of ^ to node =6585.78 days. 

The difference is but a fraction of a day ; and if the sun and. 
moon were at the node in the first instance, they would be only 
20' from the node at the expiration of the period, and the dif- 
ference in the moon's latitude less than 2'; and, therefore, the 
eclipse at the close of this period must be nearly of the same 
magnitude as the eclipse at the beginning ; and hence, the 
expression "a return of the eclipse," as though the same eclipse 
could occur twice. 

This period was early discovered by the Chaldean astrono- 
mers, and hence, it is sometimes called the Chaldean period, 
and by it they were enabled to give general and indefinite 
predictions of eclipses that were to happen ; and by it any 
learner, however crude his mathematical knowledge, can desig- 
nate the day on which an eclipse will occur, from simply know- 
ing the date of some former eclipse. 

The period of 6585 days is 18 years (including four leap 
years) and 1 1 days over. 

Therefore, if we add 18 years and 11 days to the date of 
some former eclipse, we shall come within one day of the time 
of an eclipse — and it will be an eclipse of about the same mag- 
nitude as the one we reckon from. 



In the year 
Add 


EX AMP LE S. 

1806 16 June, the sun was eclipsed. 
18 11 


Add 


1824 27 June, the sun was eclipsed. 
18 10 







How near do 19 revolutions of the sun to the node correspond to 223 lu- 
nations ? What is meant by the Chaldean period ? What is its length and 
its use? An eclipse of the moon occurred July 1st, 1852 ; when may we 
look for another ? 



160 ELEMENTARY ASTRONOMY. 

1842 8 July, the sun was eclipsed. 
Add 18 10 



— (In this period are 5 leap years.) 

1860 18 July, the sun will be eclipsed. 
Add 18 11 



1878 29 July, the sun will be eclipsed. 

And thus we might go on over a great number of periods. 

The present year, 1854, May 26, a very remarkable eclipse 
of the sun will appear as visible in the north eastern part of 
the United States. From this we can predict the days for some 
future eclipses, as follows : 

1854 26 May. 
Add 18 11 



1872 6 June, the sun will be eclipsed. 
Add 18 11 



1890 17 June, the sun will be eclipsed. 

Thus we might go on, forward or backward, but to deter- 
mine on what portion of the earth any future eclipse will be 
visible, we must compute the time of day when the moon 
changes, and other circumstances, which in this work we do 
not pretend, to take into account. 

These periods will not occur continually, because the returns 
are not exact, and the small variations which occur at each 
period, will gradually wear the eclipse away, and another 
eclipse will as gradually come on and take its place. 

In respect to these periods, those eclipses which take place 
about the moon's ascending node, commence near the north 
pole, and at each period come a little further south, and finally 
leave the earth at the south pole, after the lapse of 96 periods, 
or about 1729 years. 

Will an eclipse occur continually at periods of 18 years and 11 days ? 
How many periods arc required to work one of these periods oTer the earth? 



ECLIPSES. 161 

Those eclipses which take place about the moon'3 descending 
node, commence near the south pole and pass over the earth to 
the northward, in the same interval of time. 

Eclipses of the moon are visible at all places where the moon 
is above the horizon, from the time the moon enters the earth's 
shadow until it leaves it; but eclipses of the sun are visible 
only to a limited distance from the center of the moon's shadow, 
and that limit does not exceed 60° on the earth. Eclipses of 
the sun, which occur in March, pass over the earth in a north- 
easterly direction; those which occur in September, pass over 
the earth in a southeasterly direction ; and those which occur 
in June and December, pass over in nearly an eastern direction. 

The moon eclipses other heavenly bodies as well as the sun. 
In its passage through the heavens the moon must occasionally 
pass between us and the planets, and between us and all those 
fixed stars that are situated within 6° of the ecliptic on either 
side. For in the period of 18 years, the moon must some time 
or other cover each portion of this space in the heavens. 

Such eclipses are called occultations, and if we include all the 
stars from the first to the sixth magnitude, about 40 occultations 
take place each month, and on an average about two are visible 
from any one point each month. Unless it be an occasional 
eclipse of some of the larger planets by the moon, occultations 
are not visible to the naked eye, as the light of the moon 
obscures that of the stars, when the moon is near them, and 
therefore none but astronomers who have telescopes, can ob- 
serve these eclipses, and no others seem to be aware of their 
existence. 

A list of occultations can be found each year in the English 
Nautical Almanac. 

In "what direction do solar eclipses pass over the earth ? Does the moon 
eclipse other bodies than the sun ? What are occultations, and about how 
many occur each month ? 

14 



162 ELEMENTARY ASTRONOMY. 

CHAPTER III. 
THE TIDES. 

The alternate rise and fall of the surface of the sea, as ob- 
served at all places directly connected with the waters of the 
ocean, is called tide ; and before its cause was definitely known, 
it was recognized as having some hidden and mysterious connec- 
tion with the moon, for it rose and fell twice in every lunar day. 
High water and low water had no connection with the hour of 
the day, but it always occurred in about such an interval of time 
after the moon had passed the meridian. 

When the sun and moon were in conjunction, or in opposition, 
the tides were observed to be higher than usual. 

When the moon was nearest the earth, in her perigee, other 
circumstances being equal, the tides were observed to be higher 
than when, under the same circumstances, the moon was in her 
apogee. 

The space of time from one tide to another, or from high 
water to high water (when undisturbed by wind), is 12 hours 
and about 24 minutes, thus making two tides in one lunar day ; 
showing high water on opposite sides of the earth at the same 
time. 

The declination of the moon, also, has a very sensible influ- 
ence on the tides. When the declination is high in the north, 
the tide in the northern hemisphere, which is next to the moon, 
is greater than the opposite tide ; and when the declination of 
the moon is south, the tide opposite to the moon is greatest. 

It is considered mysterious, by most persons, that the moon 

Give a definition of tides. What connection was observed, in early 
times, between the moon and times of high water? When were tides 
higher than usual? What is the time from one high tide to another? 



THE TIDES. 



163 



by its attraction should be able to raise a tide on the opposite 
side of the earth. 

That the moon should attract the water on the side of the 
earth next to her, and thereby raise a tide, seems rational and 
natural, but that the same simple action also raises the oppo- 
site tide, is not as readily admitted ; and, in the absence of clear 
illustration, it has often excited mental rebellion — and not a 
few popular lecturers have attempted explanations from false 
and inadequate causes. 

But the true cause is the sun and moon's attraction ; and 
until this is clearly and decidedly 
understood — not merely assented 
to, but fully comprehended — it is 
impossible to understand the com- 
mon results of the theory of gravity, 
which are constantly exemplified in 
the solar system. 

We now give a rude, but striking, 
and we hope, a satisfactory expla- 
nation. 

Conceive the frame -work of the 
earth to be an inflexible solid, as it 
really is, composed of rock, and in- 
capable of changing its form under 
any degree of attraction ; conceive 
also that this solid protuberates out 
of the sea, at opposite points of the 
earth, at A and B, as represented 
in the figure, A being on the side of 
the earth next to the moon, m, and 
B opposite to it. Now, in connec- 
tion with this solid, conceive a great 
portion of the earth to be composed 




What is the true course of the tides ? Explain the true cause of the tide 
rising on the side of the earth opposite the moon ? 



164 ELEMENTARY ASTRONOMY. 

of water, whose particles are inert, but readily move among 
themselves. 

The solid AB cannot expand under the moon's attraction, 
and if it move, the whole mass moves together, in virtue of 
the moon's attraction on its center of gravity. But the particles 
of water at a, being free to move, and being under a more 
powerful attraction than the center of the solid, rise toward A, 
producing a tide. 

The particles of water at b being less attracted toward m than 
the center of the solid, will not move toward m as fast as the 
solid, and being inert, they will be, as it were, left behind. The 
solid is drawn toward the moon more powerfully than the parti- 
cles of water at h, and the solid sinks in part into the water, 
but the observer at B, of course, conceives it the water rising 
upon the shore (which in effect it is), thereby producing a tide. 

Mathematicians have found, by analytical investigation, that 
the power of the moon's attraction to produce the tides, varies 
as the inverse cube of the distance to the moon. 

The sun's attraction on the earth is vastly greater than that 
of the moon ; but by reason of the great distance to the sun, 
that body attracts every part of the earth nearly alike, and, 
therefore, it has much less influence in raising a tide than the 
moon. 

From a long course of observations made at Brest, in France, 
it has been decided that the medium high tides, when the sun 
and moon act together in the svzigies, is 19.317 feet; and 
when they act against each other (the moon in quadrature), 
the tides are only 9.151 feet. Hence the efficacy of the moon, 
in producing the tides, is to that of the sun, as the number 
14.23 to 5.08.* 

* These numbers are found as follows : Let m represent the effective 
force of the moon, and s that of the sun. 

Then m-j-?=l9.317, and m—s^ 9.151. 
Whence m= 14.23, and s=5.08. 

Is the sun's attraction on the eartli greater than that of the moon ? If 
bo, why do we not have greater tides from the action of the sun than from 
the action of the moon '? 



THE TIDES. 1G5 

Among the islands in the Pacific ocean, observations give 
the proportion of 5 to 2.2, for the relative influences of these 
two bodies; and, as this locality is more favorable to accuracy 
than that of Brest, it is the proportion generally taken. 

Having the relative influences of two bodies in raising the 
tides, we have the relative masses of those two bodies, pro- 
vided they were at the same distance. But the influence of 
the moon on the tides has a variation corresponding with the 
inverse cube of the distance, and the distance to the sun is 
397.2 times the mean distance to the moon. Hence, to have 
the influence of the moon on the tides, when that body is 
removed to the distance of the sun, we must divide its od- 
served influence by the cube of 397.2. That is, the mass of 

the moon, is to the mass of the sun, as the number ; — 

(397.2) 3 

is to the number 2.2. 

If the mass of the earth is assumed to be unit}/, the mass 

of the sun, is found by its attraction, to be 354945; and now 

if we represent the mass of the moon by m, we shall have the 

following proportion : 

m : 354945 : 



(397. 2) a 

This proportion makes m, the mass of the moon, to be nearly 
^y. The more correct value is ^, computed from other and 
more reliable data, which is to be found in our larger work. 

The time of high water at any given point is not commonly 
at the time the moon is on the meridian, but two or three hours 
after, owing to the inertia of the water ; and places, not far 
from each other, have high water at very different times on the 
same day, according to the distance and direction that the tide 
wave has to undulate from the main ocean. 

The interval between the meridian passage of the moon and 
the time of high water, is nearly constant at the same place. 
It is about fifteen minutes less at the syzigies than at the quad- 
Is the time of high Tfater when the moon is on the meridian '■ 



166 ELEMENTARY ASTRONOMY. 

ratures ; but whatever the mean interval is at any place, it is 
called the establishment of the port. 

It is high water at Hudson, on the Hudson river, before it is 
high water at New York, on the same day ; but the tide wave 
that makes high water one day at Hudson, made high water at 
New York the day before ; and the tide waves that make high 
water now, were, probably, raised in the ocean several days 
ago ; and the tides would not instantly cease on the annihilation 
of the sun and moon. 

The actual rise of the tide is very different in different places, 
being greatly influenced by local circumstances, such as the 
distance and direction to the main ocean, the shape and depth 
of the bay or river, &c. &c. 

In the Bay of Fundy the tide is sometimes fifty and sixty 
feet ; in the Pacific ocean, it is about two feet ; and in some 
places in the West Indies, it is scarcely fifteen inches. In in- 
land seas and lakes there are no tides, because the moon's attrac- 
tion is equal, or nearly so, over their whole extent of surface. 

The following table shows the hight of the tides at the most 
important points along the coast of the United States, as ascer- 
tained by recent observation : 

Feet. 

Annapolis, (Bay of Fundy), 60 

Apple River, 50 

Chicneito Bay, (north part of the Bay of Fundy,). 60 

Passamaquoddy River, 25 

Penobscot River, 10 

Boston, 11 

Providence, R. I., 5 

New Bedford, 5 

New Haven, 8 

New York, 5 

Cape May, , 6 

Cape Henry, 4£ 

Why do we have no tides on inland seas and lakes ? What is meant by 
the establishment of the port ? 



COMETS. 1G7 



CHAPTER IV. 



ON COMETS. 

Besides the planets, and their satellites, there are great 
numbers of other bodies, which gradually come into view, 
increasing in brightness and velocity, until they attain a max- 
imum, and then, as gradually diminish, pass off, and are lost 
in the distance. 

" These bodies are comets. From their singular and unusual 
appearance, they were for a long time objects of terror to man- 
kind, and were regarded as harbingers of some great calamity. 

" The luminous train which accompanied them was particu- 
larly alarming, and the more so in proportion to its length. It 
is but little more than half a century since these superstitious 
fears were dissipated by a sound philosophy ; and comets, 
being now better understood, excite only the curiosity of 
astronomers and of mankind in general. These discoveries, 
which give fortitude to the human mind, are not among the 
least useful. 

" It was formerly doubted whether comets belonged to the 
class of heavenly bodies, or were only meteors engendered for- 
tuitously in the air, by the inflammation of certain vapors. 
Before the invention of the telescope, there were no means of 
observing the progressive increase and diminution of their 
light. They were seen but for a short time, and their appear- 
ance and disappearance took place suddenly. Their light and 
vapory tails, through which the stars were visible, and their 
whiteness often intense, seemed to give them a strong resem- 

What is the general appearance of a comet ? Like the planets, are they 
observed to traverse the whole circumference of the heavens., or do they 
appear only for a season, in limited spaces? 



168 ELEMENTARY ASTRONOMY. 

blance to those transient fires, which we call shooting stars. 
Apparently, they differed from these only in duration. They 
might be only composed of a more compact substance capable 
of retarding for a longer time their dissolution. But these 
opinions are no longer maintained ; more accurate observations 
have led to a different theory. 

" All the comets hitherto observed have a small parallax, 
which places them far beyond the orbit of the moon ; they are 
not, therefore, formed in our atmosphere. Moreover, their ap- 
parent motion among the stars is subject to regular laws, which 
enable us to predict their whole course from a small number of 
observations. This regularity and constancy evidently indicate 
durable bodies ; and it is natural to conclude that comets are 
as permanent as the planets, but subject to a different kind of 
movement. 

"When we observe these bodies with a telescope, they re- 
semble a mass of vapor, at the center of which is commonly 
seen a nucleus, more or less distinctly terminated. Some, 
however, have appeared to consist of merely a light vapor, 
without a sensible nucleus, since the stars are visible through 
it. During their revolution, they experience progressive varia- 
tions in their brightness, which appear to depend upon their 
distance from the sun, either because the sun inflames them 
by its heat, or simply on account of a stronger illumination. 
When their brightness is greatest, we may conclude from this 
very circumstance that they are near their perihelion. Their • 
light is at first very feeble, but becomes gradually more vivid, 
until it sometimes surpasses that of the brightest planets ; after 
which it declines by the same degrees until it becomes imper- 
ceptible. We are hence led to the conclusion that comets, 
coming from the remote regions of the heavens, approach, in 
many instances, much nearer the sun than the planets, and 
then recede to much greater distances." 

How is it known that some comets are merely vapor ? Do comets in- 
crease and decrease in real brightness? 



COMETS. 169 

The following figure we give to illustrate the foregoing de- 
scription. 




"Since comets are bodies which seem to belong to our 
planetary system, it is natural to suppose that they move about 
the sun like planets, but in orbits extremely elongated. These 
orbits must, therefore, still be ellipses, having their foci at the 
center of the sun, but having their major axes almost infinite, 
especially with respect to us, who observe only a small portion 
of the orbit, namely, that in which the comet becomes visible 
as it approaches the sun. Accordingly, the orbits of comets 
must take the form of a parabola, for we thus designate the 
curve into which the ellipse passes, when indefinitely elongated. 

"About 120 comets have been calculated upon the theory 
of the parabolic motion, and the observed places are found to 
answer to such a supposition. We can have no doubt, there- 
fore, that this is conformable to the law of nature. We have 
thus obtained precise knowledge of the motions of these bodies, 
and are enabled to follow them in space. This discovery has 
given additional confirmation to the laws of Kepler, and led to 
several other important results. 

Are the orbits of the comets elliptical or parabolic ? If not parabolic, 
why are computations made on that hypothesis ? Do the comets all move 
in the S3me direction as the planets ? 

15 



170 ELEMENTARY ASTRONOMY. 

" Comets do not all move from west to east like the planets. 
Some have a direct, and some a retrograde motion. 

" Their orbits are not comprehended within a narrow zone 
of the heavens, like those of the principal planets. They vary 
through all degrees of inclination. There are some whose 
planes nearly coincide with that of the ecliptic, and others have 
their planes nearly perpendicular to it. 

" It is farther to be observed that the tails of comets begin to 
appear, as the bodies approach near the sun ; their length in- 
creases with this proximity, and they do not acquire their 
greatest extent, until after passing the perihelion. The direc- 
tion is generally opposite to the sun, forming a curve slightly 
concave, the sun on the concave side. 

U The portion of the comet nearest to the sun must move 
more rapidly than its remoter parts, and this will account for 
the lengthening of the tail. 

" The tail, however, is by no means an invariable appendage 
of comets. Many of the brightest have been observed to have 
short and feeble tails, and not a few have been entirely without 
them. Those of 1585 and 1763 offered no vestige of a tail; 
and Cassini describes the comet of 1682 as being as round and 
as bright as Jupiter. On the other hand, instances are not 
wanting of comets furnished with many tails, or streams of 
diverging light. That of 1744 had no less than six, spread 
out like an immense fan, extending to a distance of nearly 30 
degrees in length* 

" The smaller comets, such as are visible only in telescopes, 
or with difficulty by the naked eye, and which are by far the 
most numerous, offer very frequently no appearance of a tail, 
and appear only as round or somewhat oval vaporous masses. 
more dense toward the center ; where, however, they appear to 
have no distinct nucleus, or any thing which seems entitled to 
be considered as a solid body. 

"The tail of the comet of 1456 was 60 degrees long. That 

Mention the apparent lengths of the tails of some of the comets ? Do 
any of the comets have more than one tail ? 



COMETS. 171 

of 1618, 100 deorees, so that its tail had not all risen when its 
head reached the middle of the heavens. The comet of 1680 
was so great, that though its head set soon after the sun, its 
tail, 70 degrees long, continued visible all night. The comet of 
1689 had a tail 68 degrees long. That of 1769 had a tail more 
than 90 degrees in length. That of 1811 had a tail 23 degrees 
long. The recent comet of 1 843 had a tail 60 degrees in length. 

" When we have determined the elements of a comet's orbit, 
we compare them with those of comets before observed, and 
see whether there is an agreement with respect to any of them. 
If there is a perfect identity as to the elements, we should have 
no hesitation in concluding that they belonged to different ap- 
pearances of the same comet. But this condition is not rigor- 
ously necessary ; for the elements of the orbit may, like those 
of other heavenly bodies, have undergone changes from the 
perturbations of the planets, or from their mutual attractions. 
Consequently, we have only to see whether the actual elements 
are nearly the same with those of any comet before observed, 
and then, by the doctrine of chances, we can judge what re- 
liance is to be placed upon this resemblance. 

"Dr. Halley remarked that the comets observed in 1531, 
1607, 1682, had nearly the same elements ; and he hence con- 
cluded that they belonged to the same comet, which, in 151 
years, made two revolutions, its period being about 76 years. 
It actually appeared in 1759, agreeably to the prediction of 
this great astronomer ; and again in 1 835, by the computation 
of several eminent astronomers. According to Kepler's third 
law, if we take for unity half the major axis of the earth's 
orbit, the mean distance of this comet must be equal to the 
cube root of the square of 76, that is, to 17.95. The major 
axis of its orbit must, therefore, be 35.9 ; and as its observed 
perihelion distance is found to be 0.58, it follows that its aphe- 
lion distance is equal to 35.32. It departs, therefore, from the 
sun to thirty-five times the distance of the earth, and after- 

From what data do astronomer.-? predict the return of comets? 



172 ELEMENTARY ASTRONOMY. 

ward approaches nearly twice as near the sun as the earth is, 
thus describing an ellipse extremely elongated. 

" The intervals of its return to its perihelion are not con* 
stantly the same. That between 1531 and 1607 was three 
months longer than that between 1607 and 1682; and this 
last was 18 months shorter than the one between 1682 and 
1759. It appears, therefore, that the motions of comets are 
subject to perturbations, like those of the planets, and to a 
much more sensible degree. 

" Comets, in passing among and near the planets, are mate- 
rially drawn aside from their courses, and in some cases, have 
their orbits entirely changed. This is remarkably the case 
with Jupiter, which seems, by some strange fatality, to be 
constantly in their way, and to serve as a perpetual stumbling- 
block to them. In the case of the remarkable comet of 1770, 
which was found by Lexell to revolve in a moderate ellipse in 
the period of about five years, and whose return was predicted 
by him accordingly, the prediction was disappointed by the 
comet actually getting entangled among the satellites of Jupiter, 
and being completely thrown out of its orbit by the attraction 
of that planet, and forced into a much larger ellipse. By this 
extraordinary renconter, the motions of the satellites suffered not 
the least perceptible derangement — a sufficient proof of the small- 
ness of the comet's mass." 

The comet of 1456, represented as having a tail of 60° in 
length, is now found to be Halley's comet, which has made 
several returns — in 1531, 1607, 1682, 1759, and recently, in 
1835. In 1607 the tail was said to have been over 30 degrees 
in length; but in 1835 the tail did not exceed 20 degrees. 
Does it lose substance, or does the matter composing the tail 
condense ? or, have we received only exaggerated and dis- 
torted accounts from the earlier times, such as fear, superstition, 
and awe, always put forth? "We ask these questions, but can- 
not answer them. 

Does the same comet return at equal intervals? and if not, why? What 
circumstances show us that comets have small masses ? 



COMETS. 



17! 



" Professor Kendall, in his Uranography, speaking of the 
fears occasioned by comets, says : Another source of appre- 
hension, with regard to comets, arises from the possibility of 
their striking our earth. It is quite probable that even in the 
historical period, the earth has been enveloped in the tail of a 
comet. It is not likely that the effect would be sensible at the 
time. The actual shock of the head of a comet against the 
earth is extremely improbable. It is not likely to happen once 
in a million of years. 

" If such a shock should occur, the consequences might 
perhaps be very trivial. It is quite possible that many of the 
comets are not heavier than a single mountain on the surface 
of the earth. It is well known that the size of mountains on 
the earth is illustrated by comparing them to particles of dust 
on a common globe." 

The following cut represents a telescopic view of the comet 
of 1811: 




Is there a possibility that a comet may strike the earth ? If such a thing 
should occur, would it cause the destruction of the earth ? 



174 ELEMENTARY ASTRONOMY. 

CHAPTER V. 
ONTHE PECULIARITIES OF THE FIXED STARS. 

For the facts as contained in the subject matter of this 
chapter, we must depend wholly on authority ; for that reason 
we give only a compilation, made in as brief a manner as the 
nature of the subject will admit. 

In the first part of this work it was soon discovered that the 
fixed stars were more remote than the sun or planets ; and now, 
having determined their distances, we may make further in- 
quiries as to the distances to the stars, which will give some 
index by which to judge of their magnitudes, nature, and 
peculiarities. 

" It would be idle to inquire whether the fixed stars have a 
sensible parallax, when observed from different parts of the 
earth. We have already had abundant evidence that their dis- 
tance is almost infinite. It is only by taking the longest base 
accessible to us, that we can hope to arrive at any satisfactory 
result. 

"Accordingly, we employ the major axis of the earth's orbit, 
which is nearly 200 millions of miles in extent. By observing 
a star from the two extremities of this orbit, at intervals of six 
months, and applying a correction for all the small inequalities, 
the effect of which we have calculated, we shall know whether 
the longitude and latitude are the same or not at these two 
epochs. 

" It is obvious, indeed, that the star must appear more ele- 
vated above the plane of the ecliptic when the earth is in the 
part of its orbit which is nearest to the star, and more de- 
pressed when the contrary takes place. The visual rays drawn 

What base is taken to measure the distance to the fixed stars? Do the 
fixed stars appear in the same direction from each extremity of this base? 
And 5f so, what does that prove? 



PECULIARITIES OF THE FIXED STARS. 175 

from the earth to the star, in these two positions, differ from 
the straight line drawn from the star to the center of the earth's 
orbit ; and the angle which either of them forms with this 
straight line, is called the annual parallax. 

" As the earth does not pass suddenly from one point of its 
orbit to the opposite, but proceeds gradually, if we observe the 
positions of a star at the intermediate epochs, we ought, if the 
annual parallax is sensible, to see its effects developed in the 
same gradual manner. For example, if the star is placed at 
the pole of the ecliptic, the visual rays drawn from it to the 
earth, will form a conical surface, having its apex at the star, 
and for its base, the earth's orbit. This conical surface being 
produced beyond the star, will form another opposite to the 
first, and the intersection of this last with the celestial sphere, 
will constitute a small ellipse, in which the star will always 
appear diametrically opposite to the earth, and in the prolonga- 
tion of the visual rays drawn to the apex of the cones. 

4< But notwithstanding all the pains that have been taken to 
multiply observations, and all the care that has been used to 
render them perfectly exact, we have been able to discover 
nothing which indicates, with certainty, even the existence of 
an annual parallax, to say nothing of its magnitude. Yet the 
precision of modern observations is such, that if this parallax 
were only 1", it is altogether probable that it would not have 
escaped the multiplied efforts of observers, and especially those 
of Dr. Bradley, who made many observations to discover it, 
and who, in this undertaking, fell unexpectedly upon the phe- 
nomena of aberration* and nutation. These admirable dis- 
coveries have themselves served to show, by the perfect agree- 
ment which is thus found to take place among observations, 
that it is hardly to be supposed that the annual parallax can 
amount to 1". The numerous observations on the polar star, 
employed in measuring an arc of the meridian, through France, 

* Subjects which will come in the next chapter. 

What is meant by annual parallax ? Has such a parallax been observed? 
And if not, why? 



176 ELEMENTARY ASTKOXOMY. 

have been attended with a similar result, as to the amount of 
the annual parallax. From all this we may conclude, that as 
yet there are strong reasons for believing that the annual par- 
allax is less than 1", at least with respect to the stars hitherto 
observed. 

" Thus the semi-diameter of the earth's orbit, seen from the 
nearest star, would not appear to subtend an angle of 1"; and 
to an observer placed at this distance, our sun, with the whole 
planetary system, would occupy a space scarcely exceeding the 
thickness of a spider's thread. 

"It is evident that the stars undergo considerable changes, 
since these changes are sensible even at the distance at which 
we are placed. There are some which gradually lose their 
light, as the star g of Ursa Major. Others, as ft of Cetus, be- 
come more brilliant. Finally, there are some which have been 
observed to assume suddenly a new splendor, and then gradually 
fade away. Such was the new star which appeared in 1572, in 
the constellation Cassiopeia. It became all at once so brilliant 
that it surpassed the brightest stars, and even Venus and Jupi- 
ter, when nearest the earth. It could be seen at mid-day. 
Gradually this great brilliancy began to diminish, and the star 
disappeared in sixteen months from the time it was first seen, 
without having changed its place in the heavens. Its color, 
during this time, suffered great variations. At first it was of a 
dazzling white, like Venus ; then of a reddish yellow, like 
Mars and Aldebaran ; and lastly, of a leaden white, like Saturn. 
Another star which appeared suddenly in 1604, in the con- 
stellation Serpentarius, presented similar variations, and dis- 
appeared after several months. These phenomena seem to 
indicate vast flames, which burst forth suddenly in these great 
bodies. Who knows that our sun may not be subject to sim- 
ilar changes, by which great revolutions hive perhaps taken 
place in the state of our globe, and are yet to take place. 

" Some stars, without entirely disappearing, exhibit varia- 

Do the fixed stars undergo any changes? What is said of new star*., 
and in what constellations did they happen? 



PECULIARITIES OF THE FIXED STARS. 177 

tions not less remarkable. Their light increases and decreases 
alternately, in regular periods. They are called, for this reason, 
variable stars. Such is the star Algol, in the head of Medusa, 
which has a period of about three days ; ^ of Cepheus, which 
has one of five days ; § of Lyra, six ; v of Antinous, seven ; 
o of Cetus, 334 ; and many others. 

" Several attempts have been made to explain these period- 
ical variations. It is supposed that the stars which are subject 
to them, are, like to all the other stars, self-luminous bodies, 
or true suns, turning on their axes, and having their surfaces 
partly covered with dark spots, which may be supposed to 
present themselves to us at certain times only, in consequence 
of their rotation. Other astronomers have attempted to account 
for the facts under consideration by supposing these stars to 
have a form extremely oblate, by which a great difference would 
take place in the light emitted by them under different aspects. 
Lastly, it has been supposed that the effect in question is owing 
to large opake bodies, revolving about these stars, and occa- 
sionally intercepting a part of their light. Time, and the mul- 
tiplication of observations, may perhaps decide which of these 
hypotheses is the true one. 

One of the best methods of observing these phenomena is 
to compare the stars together, designating them by letters or 
numbers, and disposing of them in the order of their brilliancy. 
If we find, by observation, that this order changes, it is a 
proof that one of the stars thus compared, has likewise changed; 
and a few trials of this kind will enable us to ascertain which 
it is that has undergone a variation. In this manner, we can 
only compare each star with those which are in the neighbor- 
hood, and risible at the same time. But by afterward com- 
paring these with others, we can, by a series of intermediate 
terms, connect together the most distant extremes. This 
method, which is now practiced, is far preferable to that of the 
ancient astronomers, who classed the stars after a very vague 

What is understood by variable stars? How have astronomers at- 
tempted to account for these appearances? 



178 ELEMENTARY ASTRONOMY. 

comparison, according to what they called the order of their 
magnitudes, but which was, in reality, nothing but that of their 
brightness, estimated in a very imperfect manner." 

DOUBLE AND MULTIPLE STARS. 

" There are stars which, when viewed by the naked eye, and 
even by the help of a telescope of moderate power, have the 
appearance of only a single star ; but, being seen through a 
good telescope, they are found to be double, and in some cases, 
a very marked difference i3 perceptible, both as to their bril- 
liancy and the color of their light. These Sir "VV. Herschel 
supposed to be so near each other, as to obey, reciprocally, the 
power of each other's attraction, revolving about their common 
center of gravity, in certain determinate periods. 



Castor. y Leonis. Rigel. Pole Star, n Monoc. £ Cancri. 

" The two stars, for example, which form the double star 
Castor, have varied in their angular situation more than 45° 
since they were observed by Dr. Bradley, in 1759, and appear 
to perform a retrograde revolution in 342 years, in a plane per- 
pendicular to the direction of the sun. Sir W. Herschel found 
them in intermediate angular positions, at intermediate times, 
but never could perceive any change in their distance. The 
retrograde revolution of y in Leo, another double star, is sup- 
posed to be in a plane considerably inclined to the line in which 
we view it, and to be completed in 1200 years. The stars s of 
Bootes, perform a direct revolution in 1681 years, in a plane 
oblique to the sun. The stars } of Serpens, perform a retro- 
grade revolution in about 375 years ; and those of y in Virgo 
in 708 years, without any change of their distance. In 1802, 
the large star £of Hercules, eclipsed the smaller one, though 

What is understood by double stars? Do double stars revolve about 
each other ? Mention the times of revolution of some of them. 



PECULIARITIES OF THE FIXED STARS. 179 

they were separate in 1782. Other stars are supposed to be 
united in triple, quadruple, and still more complicated systems. 
" With respect to the determination of the real magnitude 
of the stars, and their respective distances, we have as yet 
made but little progress. Researches of this kind must be 
left to future astronomers. It appears, however, that the stars 
are not uniformly distributed over the heavens, but collected 
into groups, each containing many millions of stars. We can 
form some idea of them, from those small whitish spots called 
Nebulae, which 
appear in the 
heavens as rep- 
resented in the 
accompanying 
illustration. 
By means of 
the telescope, 
we distinguish 
in these collec- 
tions an almost 
infinite number 
of small stars, 

so near each other, that their rays are ordinarily blended by 
irradiation, and thus present to the eye only a faint uniform 
sheet of light. That large, white, luminous track, which tra- 
verses the heavens from one pole to the other, under the name 
of the Milky Way, is probably nothing but a nebula of this 
kind, which appears larger than the others, because it is nearer 
to us. With the aid of the telescope we discover in this zone 
of light such a prodigious number of stars that the imagination 
is bewildered in attempting to represent them. Yet, from the 
angular distances of these stars, it is certain that the space 
which separates those which seem nearest to each other, is at 
least a hundred thousand times as great as the radius of the 

What is meant by Nebulae ? What is said of the Milky Way? What is 
its appearance through a telescope ? 




180 ELEMENTARY ASTRONOMY. 

earth's orbit. This will give us some idea of the immense 
extent of the group. To what distance then must we with- 
draw, in order that this whole collection may appear as small 
as the other nebulae which we perceive, some of which cannot, 
by the assistance of the best telescopes, be made to present 
any thing but a bright speck, or a simple mass of light, of the 
nature of which we are able to form some idea only by analogy? 
"When we attempt, in imagination, to fathom this abyss, it is in 
vain to think of prescribing any limits to the universe, and the 
mind reverts involuntarily to the insignificant portion of it 
which we are destined to occupy." 

■ Before we close this chapter, we think it important to call 
the attention of the reader to Table II, in which will be seen, 
at a glance (in the columns marked annual variation), the gen- 
eral effect of the precession of the equinoxes ; we here notice 
that all the stars, from the 6th to the 18th hour of right ascen- 
sion, have a progressive motion to the southward ( — ), and all 
the stars from the 18th to the 6th hour of right ascension, have 
a progressive motion to the northward (-|-), and the greatest 
variations are at Oh. and 12h. But these motions are not, in 
reality, the motions of the stars ; they result from motions of 
the earth. Whenever the annual motion of any star does not 
correspond with this common displacement of the equinox, we 
say the star has a proper motion ; and by such discrepancy it 
has been decided, that those stars marked with an asterisk, in 
the catalogue, have proper motions; and the star 61 Cygni, 
near the close of the table, has the greatest proper motion. 

From this circumstance, and from the fact of its being a 
double star, it was selected by Bessel as a fit subject for the 
investigation of stellar parallax ; and it is now contended, and 
in a measure granted, that the annual parallax of this star is 
0".35, which makes its distance more than 592,000 times the 
radius of the earth's orbit ; a distance that light could not 
traverse in less than nine and one -fourth years. 

What is to be noticed in Table II ? How do astronomers determine what 
stars have a proper motion ? What is said of the star 61 Cygni ? 



ABERRATION. 181 



CHAPTER VI* 

ABERRATION, NUTATION, AND PRECESSION 
OF THE EQUINOXES. 

About the year 1725, Dr. Bradley, of the Greenwich obser- 
vatory, commenced a very rigid course of observations on the 
fixed stars, with the hope of detecting their parallax. These 
observations disclosed the fact, that all the stars which come 
to the upper meridian near midnight, have an increase of lon- 
gitude of about 20"; while those opposite, near the meridian of 
the sun, have a decrease of longitude of 20"; thus making an 
annual displacement of 40". These observations were continued 
for several years, and found to be the same at the same time 
each year ; and, what was most perplexing, the results were 
directly opposite from such as would arise from parallax. 

These facts were thrown to the world as a problem demanding 
solution, and, for some time, it baffled all attempts at explana- 
tion ; but it finally occurred to the mind of the Doctor, that it 
might be an effect produced by the progressive motion of light 
combined with the motion of the earth ; and, on strict exami- 
nation, this was found to be a satisfactory solution. 

A person standing still in a shower of rain. When the rain 
falls perpendicularly, the drops will strike directly on the top 
of his head ; but if he starts and runs in any direction, the 
drops will strike him in the face ; and the effect would be the 
same, in relation to the direction of the drops, as if the person 
stood still and the rain came inclined from the direction he ran. 

This is a full illustration of the principle of these changes 
in the positions of the stars, which is called aberration; but the 
following explanation is more appropriate. 

When and by whom was Aberration, and Nutation discovered? "Were 

such results anticipated? Illustrate aberration, 



182 



ELEMENTARY ASTRONOMY 



Conceive the rays of light to be of a material substance, and 
its particles progressive, passing from the star S to the earth 

at B ; passing directly through 
the telescope, while the telescope 
itself moves from A to B by the 
motion of the earth. And if D 
B is the motion of light, and A 
B the motion of the earth, then 
the telescope must be inclined in 
the direction of AD, to receive 
the light of the star, and the 
apparent place of the star -would 
be at S', and its true place at S, 
and the angle ADB is 20".36, at 
its maximum, called the angle 
of aberration. 

By the known motion of the 
earth in its orbit, we have the 
value of AB corresponding to 
one second of time : we have the 
angle ADB by observation : the 
angle at B is a right angle, and 
(from these data), computing 
the side BD, we have the velocity 
of light, corresponding to one 
second of time. To make the 
computation, we have 
DB : BA : : Bad. : tan. 20".36. 
But BA, the distance which the earth moves in its orbit in 
one second of time, is within a very small fraction of 19 miles; 
the logarithm of the distance is 1.378802, and, from this, we 
find that BD must be 192600 miles, the velocity of light in a 
second; a result very nearly the same as before deduced from 
observations on the eclipses of Jupiter's moons. 

What is the greatest an^le of aberration ? "What truth has been demon- 




ABERRATION. 183 

The agreement of these two methods, so disconnected and 
so widely different, in disclosing such a far-hidden and remark- 
able truth, is a striking illustration of the power of science, 
and the order, harmony, and sublimity that pervades the uni- 
verse. 

To show the effects of aberration on the whole starry heavens, 
we give the figure below. Conceive the earth to be moving in 
its orbit from A to B. The stars in the line AB, whether at 




or 180, are not affected by aberration. The stars, at right 
angles to the line AB, are most affected by aberration, and it 

When, and in what position in respect to the sun, is a star when it is 
most affected by aberration ? 



184 ELEMENTARY ASTRONOMY. 

is obvious that the general effect of aberration is to give the 
stars an apparent inclination to that part of the heavens, to- 
ward which the earth is moving. Thus the star at 90 has its 
longitude increased, and the star opposite to it, at 270, has its 
longitude decreased, by the effect of aberration ; both being 
thrown more toward 180. The effect on each star is 20".36. 
But when the earth is in the opposite part of its orbit, and 
moving the other way, from C to D, then the star at 90 is ap- 
parently thrown nearer to ; so also is the star at 270, and the 
whole annual variation of each star, in respect to longitude, is 
40".72. 

The supposition of the earth's annual motion fully explains 
aberration ; conversely, then, the observed variations of the 
stars, called aberration, are decided proofs of the earth's annual 
motion. 

In consequence of aberration, each star appears to describe 
a small ellipse in the heavens, whose semi-major axis is 20".36, 
and semi-minor axis is 20". 36 multiplied by the sine of the 
latitude of the star. The true place of the star is the center 
of the ellipse. If the star is on the ecliptic, the ellipse, just 
mentioned, becomes a straight line of 40". 72 in length. 

If the star is at either pole of the ecliptic, the ellipse be- 
comes a circle of 40".72 in diameter, in respect to a great 
circle; but a circle, however small, around the pole, will in- 
clude all degrees of longitude ; hence it is possible for stara 
very near either pole of the ecliptic, to change longitude very 
considerably, each year, by the effect of aberration ; but no 
star is sufficiently near the pole to cause an apparent revolution 
round the pole by aberration ; and the same is true in relation 
to the poles of the celestial equator. 

All these ellipses have their longer axis parallel to the ecliptic, 
and for this reason it is easy to compute the aberration of a 
star in latitude and longitude, but it is a far more complex 

What does aberration explain ? What is the apparent motion of a star 
on the ecliptic in consequence of aberration? What is the apparent motion 
of other stars? 



NUTATION. IPS 

problem to compute the effects in respect to right ascension 
and declination. 

The effects of aberration on the moon, are too small to be 
noticed, as light passes that distance in about one second of 
time. 

NUTATION. 

While Dr. Bradley was continuing his observations to verify 
his theory of aberration, he observed other small variations, in 
the latitudes and declinations of the stars, that could not be 
accounted for on the principle of aberration. 

The period of these variations was observed to be about the 
same as the revolution of the moon's node, and the amount of 
the variation corresponded with particular situations of the 
node ; and, in short, it was soon discovered that the cause of 
these variations was a slight vibration in the earth's axis, 
caused by the action and reaction of the sun and moon on the 
protuberant mass of matter about the equator, which gives 
the earth its spheroidal form, and the effect itself, is called 
Nutation. 

To illustrate this subject, we give the following figure on the 
next page. Let m represent the moon, or any body of matter; 
its attraction on the ring has a tendency to cause the plane of 
the ring to incline towards the attracting body, m. Let the 
plane of the ring, in the figure, also be the plane of the equator, 
and the ring the protuberant mass of matter around the equator. 
Let m be the moon at its greatest declination, and, of course, 
without the plane of the ring. 

Let P be the polar star. The attraction of m on the ring- 
inclines it to the moon, and causes it to have a slight motion 
on its center ; but the motion of this rinfif is the motion of the 
whole earth, which must cause the earth's axis to change its 
position in relation to the star P, and in relation to all the 
stars. 

What are the small vibrations of the stars, in latitude and declination, 
called ? What is the period of these vibrations ? What causes them ? 
16 



186 ELEMENTARY ASTRONOMY. 

When the moon is on the other side of the ring, that is, 
opposite in declination, the effect is to incline the equator to 
the opposite direction, which must be, and is, indicated by an 
apparent motion of all the stars. 




A slight alternate motion of all the stars in declination, cor~ 
responding to the declinations of the sun and moon, was care- 
fully noted by Dr. Bradley, and since his time, has been fully 
verified and definitely settled : this vibratory motion is known 
by the name of nutation, and it is fully and satisfactorily ex- 
plained on the principles of universal gravity ; and conversely, 
these minute and delicate facts, so accurately and completely 
conforming to the theory of gravity, served as one of the many 
strong points of evidence to establish the truth of that theory. 

By inspecting the figure, it will be perceived that when the 
sun and moon have their greatest northern declinations, all the 
stars north of the equator and in the same hemisphere as these 
bodies, will incline toward the equator ; or all the stars in that 

What theory is confirmed bv nutation ? 



NUTATION, 187 

hemisphere will incline southward, and those in the opposite 
hemisphere will incline northward ; the amount of vibration of 
the axis of the earth is only 9".6 (as is shown by the motion of 
the stars), and its period is 18.6, or about nineteen years, the 
time corresponding to the revolution of the moon's node. When 
the moon is in the plane of the equator, its attraction can have 
no influence in changing the position of that plane ; and it is 
evident that the greatest effect must be when the moon's decli- 
nation is greatest. 

The moon's declination is greatest when the longitude of the 
moon's ascending node is 0, or at the first point of Aries. The 
greatest declination is then 28° on each side of the equator ; 
but when the descending node is in the same point, the moon's 
greatest declination is only 18°. Hence there will be times, a 
succession of years, when the moon's action on the protuberant 
matter about the equator must be greater than in an opposite 
succession of years, when the node is in the opposite position. 
Hence, the amount of lunar nutation depends on the position 
of the moon's nodes. 

The mean course of the moon is along the ecliptic : its varia- 
tion from that line is only about five degrees on each side ; 
hence, the medium effect of the moon, on the protuberant mass 
of matter at the equator, is the same as though the moon were 
all the while in the ecliptic. But, in that case, its effect would 
be the same at every revolution of the moon ; and the earth's 
equator and axis would then have an equilibrium of position, 
and there would be no nutation, save a slight monthly nutation, 
which is too small to be sensible to observation ; and the nuta- 
tion which we observe, is only an inequality of the moon's 
attraction on the protuberant equatorial ring; and, however 
great that attraction might be, it would cause no vibration in 
the position of the earth, if it were constantly the same. 

We have, thus far, made particular mention of the moon, 
but there is also a solar nutation; its period is, of course, a year ; 

What must be the position of the moon to have the greatest effect on 
nutatiou ? In what, position does the moon have no effect on nutation ? 



188 ELUMEXTAKY ASTRONOMY. 

and it is very trifling in amount, because the sun attracts all 
parts of the earth nearly alike ; and the short period of one 
year, or half a year (which is the time that the unequal attrac- 
tion tends to change the plane of the ring in one direction), is 
too short a time to have any great effect on the inertia of the 
earth. 

The solar nutation, in respect to declination, is only one 
second. 

Hitherto we have considered only one effect of nutation — 
that which changes the position of the plane of the equator — 
or, what is the same thing, that which changes the position of 
the earth's axis ; but there is another effect, of greater magni- 
tude, earlier discovered, and better known, resulting from the 
same physical cause, — we mean the 

PRECESSION OF THE EQUINOXES. 

We again return to first principles, and consider the mutual 
attraction between a ring of matter and a body situated out of 
the plane of the ring; the effect, as we have several times 
shown, is to incline the ring to the body, or (which is the 
same in respect to relative positions), the body inclines to run 
to the plane of the ring. 

The mean attraction of the moon is in the plane of the ecliptic. 
The sun is all the while in the ecliptic. Hence, the mean 
attraction of both sun and moon is in one plane, the ecliptic ; 
but the equator, considered as a ring of matter surrounding 
a sphere, is inclined to the plane of tile ecliptic by an angle 
of 23-J- degrees, and hence the sun and moon have a constant 
tendency to draw the equator to the ecliptic, and actually do 
draw it to that plane ; and the visible effect is, to make both 
sun and moon, in revolutions, cross the equator sooner than 
they otherwise would, and thus the equinox falls back on the 
ecliptic, called the precession of the equinoxes. 

Is there a monthly nutation ? Is there a solar nutation, and how great 
is it ? What other effect arises from the attraction of the sun and moon, on 
the protuberant, mass of matter about the equator? 



PRECESSION OF THE EQUINOXES. 189 

The animal mean precession of the equinoxes is 50". 1 of arc, 
as is shown by the sua coming into the equinox, or crossing 
the equator at a point 50". 1 before it makes a revolution in 
respect to the stars. 

If the moon were all the while in the ecliptic, the precession 
of the equinoxes would then be a constantly flowing quantity, 
equal to 50". 1 for each year ; but, for a succession of about 
nine years, the moon runs out to a greater declination than the 
ecliptic, and, during that time, its action on the equatorial 
matter is greater than the mean action, and then comes a suc- 
cession of about nine years, when its action is less than its 
mean ; hence, for nine years, the precession of the equinoxes 
will be more than 50". 1 per year, and, for the nine years follow- 
ing, the precession will be less than 50". 1 for each year ; and 
the whole amount of variation, for this inequality, in respect to 
longitude, is 17".3, and its period is half a revolution of the 
moon's nodes. This inequality is called the equation of the 
equinoxes, and varies as the sine of the longitude of the moon's 
nodes. 

The precession of the equinoxes causes a variation of the 
right ascensions and declinations of all the fixed stars, as may 
be seen by inspecting the catalogue of stars in Table II. 
When any particular star is observed to have a greater or less 
variation than the quantity corresponding to the precession, 
that star is said to have a proper motion, as we have before 
observed, when treating of the stars. 

We close this volume, after calling the attention of the reader 
to our first page of tables. 

In common parlance, we say that the sun has no latitude — 
it is all the while in the ecliptic — but then it will be found 
that the sun has latitude, it deviates north and south, by a 
quantity too small even to be observed; it is, therefore, a quantity 
wholly determined by theory, and, as the sun's latitude changes 

What is the annual mean precession of the equinoxes ? Has it an equa- 
tion? and if so, to what amount ? What is the period of this equation? 



190 ELEMENTARY ASTRONOMY.. 

nearly with the latitude of the moon. we must seek for its 
cause principally in the lunar motions. * 

To understand the fact of the sun having latitude, we must 
admit that it is the center of gravity between the earth and 
moon, that moves in an elliptical orbit round the sun ; and 
that center is always in the ecliptic ; and the sun, viewed from 
that point, would have no latitude. But when the moon, m, is 
on one side of the plane of the ecliptic, SO, the earth, E, 
would be on the other side, and the sun, seen 
from the center of the earth, would appear to 
lie on the same side of the ecliptic as the moon. 
Hence, the sun will change his latitude, when the 
moon changes her latitude. 

If the moon were all the while in the plane 
of the ecliptic, the sun would have no latitude 
(save some extremely minute quantities, from the 
action of the planets, when not in the plane 
of the ecliptic); but the moon does not deviate 
more than 5° 20' from the ecliptic, and of 
course, the earth makes but a proportional de- 
viation on the other side ; but in longitude, the 
moon deviates to a right angle on both sides, 
in respect to the sun, and when the moon is in 
advance in respect to longitude, the sun appears to be in ad- 
vance also ; and when the moon is afr- her third quarter, the 
longitude of the sun is apparently thrown back by her influence: 
the greatest variation in the sun's longitude, arising from the 
motion of the earth and moon about their center of gravity, is 
about 6" each side of the mean. 



* In fact the sun is not immovably fixed in the plane of the ecliptic : it 
vibrates round the common center of gravity of the solar system. 

Jupiter is by far the most ponderous planet in the system, hence the 
center of gravity between the sun and that planet, is always extremely 
near the plane of the ecliptic, and the sun's latitude, in the Nautical Al- 
manac, is computed from the positions of the moon and Jupiter, — the result 
of each taken separately, and united. 




SEQUEL. 



A knowledge of astronomy embraces a knowledge of the 
earth as a whole, — and the external appearance of the heavens. 

The earth is very accurately represented by a globe, and the 
external appearance of the heavens can also be very accurately 
represented by the projection of each star, and the imaginary 
lines in the heavens, on a globe. 

Thus we have a terrestrial and a celestial globe. Those 
whose minds are at all cultivated, understand the terrestrial 
globe, or the globe which represents the earth, at sight, — but 
atlases and maps, of any large portions of the earth, require 
some study, as the several parts must be more or less distorted, 
as it is impossible to represent the surface of a sphere, accu- 
rately, on a plane surface. Hence, no one can comprehend 
maps, unless the mind refers them to a globe, whether the pupil 
has ever actually seen a globe, or not. 

Years ago, when spherical trigonometry was very rarely 
taught, problems on the globes were more attended to, than 
they are at present. Yet, solutions of these problems on the 
globes are very important, as they furnish a sure test of the 
comprehension of the pupil, and this is our principal object in 
giving them. 

Results obtained by the globes are, at best, but rough ap- 
proximations, and no one, properly disciplined, will claim any 
thing more for them ; but even this does not diminish their 
real importance ; for this kind of solution must go through the 
mind, to guide us through the more exact, scientific, and nu- 
merical computations. 

m 



192 SEQUEL. 



CHAPTER I. 

PROBLEMS TO BE PERFORMED ON THE TERRES- 
; TRIAL GLOBE. 

Problem 1. To find the latitude of any place. 

Rule. — Find the place on the globe, and turn the globe so as to bring 
the place to that part of the brass meridian, which is numbered from the 
equator to the poles. 

The degree marked on the meridian above the place will be the latitude. 
If the place be on the north side of the equator, the latitude will be north; 
if on the south side, the latitude is south. 

EXAMPLES. 

1. What is the latitude of the eastern point of Newfound- 
land? Am. 46° 30'. 

2. Required the latitudes of the following places : 

Florence, Italy. New York, U. S. 

Rome, Italy. Boston, U. S. 

Bencoolon, Sumatra. Havana, Cuba. 
Cadiz, Spain. Cape Town, Africa. 

Smyrna, Turkey. Buenos Ayres, S. America. 

3. "What places have no latitude? 

4. What places have no longitude? 

5. What are the latitudes of those places that have no lon- 
gitude? 

6. What places have the same length of days as the inhab- 
itants of Edinburgh? 

Am. All places that have the same latitude as Edinburgh. 
A circle round the pole in which Edinburgh is sit- 
uated, locates the places. 

7. What places have the same seasons of the year as New 
York? 



PROBLEMS ON THE GLOBES. 193 

Problem 2. To find the longitude of any place on the globe. 

Rule. — Bring the place to the brass meridian, the number of degrees on 
the equator, reckoned from the meridian which passes through Greenwich 
(England), is the longitude. 

If the globe be placed north of the operator, to the right of the brass 
meridian is east, to the left hand is west. 

Remark. Some American globes take the meridian of Washington for 
the first meridian. But all our instructions refer to the meridian of Green- 
wich, because both the English and American Nautical Almanac refer to 
that meridian. Indeed, all practical men who use the English language, 
have adopted that meridian, in whatever part of the world they are, or 
■wherever they may have been born. 

EXAMPLES. 

1. What is the longitude of St. Petersburgh? 

Ans. 30° east. 

2. What is the longitude of Cape St. Roque? 

Ans. 37° west, nearly. 

3. Required the longitudes of the fallowing places : 
Aberdeen, Scotland. Canton, China. 
Albany, U. S. Gibralter, Spain. 
Boston, U. S. Leghorn, Italy. 
Bombay, E. Indias. Muscat, Arabia, 

Problem 3. To find all those places that have the same longi' 
iude as any given place. 

Rule. — Bring the given place to the brass meridian, then all places under 
the edge of the meridian from pole to pole, have the same longitude. 

N. B. Places in the same longitude have the same hour of the day at 
the same instant of absolute time. 

EXAMPLES. 

1. What places hare the same, or nearly the same, longi- 
tude as Stockholm? 

Ans. Dantzic, Presburg, Toronto, Cape of Good Hope, &c. 

2. What inhabitants of the earth have midnight when the 
inhabitants of Jamaica have noon? 

Ans. Pekin, in China, Borneo, the western part of Australia, &c. 
17 



194 SEQUEL. 

3. What places have 7 o'clock P. M. when it is 11 o'clock 
A. M. at London? 

Ans. All places having the longitude of 90° west. 

Problem 4. To find the latitude and longitude of any 'place. 

Rule. — Bring the given place to that part of the brass meridian which is 
numbered from the equator towards the poles ; the degree above the place 
is the latitude, and the degree on the equator, cut by the brass meridian, is 
the longitude. 

N, B. This problem is but a union of the first, and second. 

EXAM PLES. 

1. What is the latitude and longitude of Cape Frio, on the 
eastern coast of South America? 

Ans. Lat. 23° S. Lon. 42° W. 

2. Find the latitudes and longitudes of the following places: 
Algiers, in Africa. Batavia, in Java. 

Aleppo, in Turkey. Belfast, in Ireland. 

Abo, in Finland. Boston, U. S. 

Calcutta, India. Cape Desolation, Greenland. 

Problem 5. Latitude and Longitude being given, to find the 
corresponding point on the globe. 

Rule. — Find the longitude of the given place on the equator, and bring 
it to that part of the brass meridian which is numbered from the equator 
to the poles ; then under the given latitude on the brass meridian, you will 
find the place. [Provided the place is marked on the globe.] 

EXAMPLES. 

1. What place has 151° east longitude, and 34° south lati- 
tude? Ans. Botanv Bay. 

2. What places have the following latitudes and longitudes? 
Lat. Lon. Lat. Lon. 

50° 6' N. 5° 54' W. 19° 26' N, 100° 6' W. 
48° 12 N. 16° 16' E. 59° 56' N. 30° 19' E. 

55°58'2sT. 3°12'W. 5° 9' S. 119° 49 E. 



PROBLEMS ON THE GLOBES. 195 

Problem 6. To find the difference of latitude between any two 
places. 

Rule. — If the two places are on the same meridian, that is, have the 
same longitude, and are both north or boih south of the equator, subtract 
one from the other, and the difference will be the difference of latitude. 
If the latitude of one of the places is north and the other south, add the 
two latitudes together, and the sum will be their difference of latitude. 

If the two places are not in the same longitude, find the latitude of 
each place by Problem 1, and subtract or add them, as above directed, 
and you will have their difference of latitude. 

EXAMPLES. 

1. What is the difference of latitude between Philadelphia 
and St. Petersburgh? Ans. 20 degrees. 

2. What difference of latitude between Greenwich and 
Cape Town, Cape of Good Hope? Ans. 85° 24'. 

3. Required the difference of latitude between the follow- 
ing places : 

London and Rome. New York and New Orleans. 

Cape Spartel and Cape Verde. Boston and Cape Horn. 
Vera Cruz and Cape Horn. Canton and Batavia. 

Problem 7. To find the least distance between any two places 
on the globe. 

Rule. — Extend a thread from one point to the other. Apply that extent 
to the equator, and find the corresponding number of degrees. Multiply 
the number of degrees thus found, by 60, for geographical miles, and by 
69.1 for English miles. 

EXAMPLES. 

1. What is the direct distance between New York and 
Liverpool? 

Ans. The length of a thread between the two places, ap- 
plied to a meridian, or to the equator, extends over 
49 degrees, as near as we can determine by sight. 
Hence the distance must be 49X60=2940 geograph- 
ical miles, or 49X69.1 = 3385.9 English miles. 



196 SEQUEL. 

2. What is the distance from Cape Cod to Cape Spartel, 
the north west point of Africa? 

Ans. 3055 geo. miles, or 3435 Eng. miles. 

3. Required the distances between the following places : 
Smyrna and Boston. London and Havana. 

Cape Town and Java Head. Rome and Paris. 
From Africa to South America — nearest points. 

Remark. Problems like the foregoing are solved by the rules of plane 
trigonometry, in works of Navigation. Every student should comprehend 
a globe sufficiently well to form, or conceive, of the spherical triangle 
formed by the latitudes and longitudes of the places : thus, for example, 

The latitude of New York is 40° 40' N. and longitude 74° W., and 
Liverpool is in latitude 53° 25' H". and 3° W. ; what triangle unites them? 

Conceive each locality to be at the angular point of a spherical triangle, 
and the north pole to be the third point. 

From the north pole to New York, is 49° 20', and to Liverpool it is 36° 
35', and the angle at the pole between these two meridians is 71°. Here, 
then, we have two sides, and the included angle of a spherical triangle, 
from which the third side can be computed, which is the distance, in 
degrees, between the two places. 



To solve some of the following problems, with or without a 
globe, the right ascension and the declination of the sun must 
be known. These elements are computed and published, an- 
nually, in the American Nautical Almanac. 

For those who have no access to an Ephemeris, we subjoin 
the following table of the sun's declination for every other day 
of the year 1858, that being the second year after leap year. 
The results in this table are given to the nearest minute of arc, 
and they will not differ many minutes for the same day, for any 
other year, for thirty or forty years to come. In short, results 
will be sufficiently near the truth to teach principles. 

The table for the sun's right ascension is given on page 6 of 
tables in this volume. 



PROBLEMS ON THE GLOBES. 



197 



SUN'S DECLINATION FOR 1858, 

But will serve for corresponding days, in other years, for the purposes 

here intended. 



D. 
1 


January. 
23° l! S 


February. 


March. 


April. 


May. 


Juue. 


17° 6' S 


7° 35' S 


4°32'N 


15° 4'N 


22° 4'N 


3 


22° 50' 


16° 31' 


6° 49' 


5 & 18' 


15° 40' 


22° 19' 


5 


22° 37' 


15° 55' 


6° 3' 


6° 4' 


16° 15' 


22° 33' 


7 


22° 23' 


15° 18' 


5° 16' 


6° 49' 


16° 49' 


22° 46' 


9 


22° 7' 


14° 40' 


4° 30' 


7° 34' 


17° 21' 


22° 57' 


11 


21° 49' 


14° V 


3° 43' 


8° 19' 


17° 53' 


23° 6' 


13 


21° 29' 


13° 21' 


2° 55' 


9° 3' 


18° 23' 


23° 14' 


15 


21° 8' 


12° 40' 


2° 8' 


9° 46' 


18° 52' 


23° 20' 


17 


20° 45' 


11° 58' 


1° 21' 


10° 28' 


19° 20' 


23° 24' 


19 
21 


20° 20' 
19° 54' 


11° 16' 
10° 33' 


33' S 


11° 10' 
11° 51' 


19° 46' 
20° 11' 


23° 27' 


14' N 


23° 27' 


23 


19° 26' 


9° 49' 


1° 2' 


12° 32' 


20° 35' 


23° 27' 


25 


18° 58' 


9° 5' 


1°49' 


13° 11' 


20° 57' 


23° 25' 


27 


18° 27' 


8° 20' 


2° 36' 


13° 50' 


21° 18' 


23° 20' 


29 


17° 56' J 




3° 23' 


14° 27' 


21° 37' 


23° 15' 



D. 

1 


July. 


August. 


Se] 


Dte'ber. 


October. 


November. 


December. 


23° 8' N 


18° 3'N 


8° 


19'N 


3° 11' S 


14° 27' S 


21° 50' S 


3 


22° 59' 


17° 32' 


7° 


35' 


3° 57' 


15° 5' 


22° 7' 


5 


22° 49' 


17° 1' 


6° 


50' 


4° 44' 


15° 42' 


22° 23' 


7 


22° 37' 


16° 28' 


6° 


6' 


5° 30' 


16° 18' 


22° 38' 


9 


22° 23' 


15° 53' 


5° 


20' 


6° 16' 


16° 53' 


22° 51' 


11 


22° 8' 


15° 18' 


4° 


35' 


7° 1' 


17° 27' 


23° 1' 


13 


21° 52' 


14° 42' 


3° 


49' 


7° 46' 


17° 59' 


23° 10' 


15 


21° 33' 


14° 5' 


3° 


3' 


8° 31' 


18° 30' 


23" 17' 


17 


21° 14' 


13° 27' 


2° 


16' 


9° 15' 


19° 0' 


23° 23' 


19 


20° 53' 


12° 49' 


1° 


30' 


9° 59' 


19° 29' 


23° 26' 


21 


20° 30' 


12° 9' 
11° 29' 




43' N 


10° 42' 
11° 25 


19° 56' 

20° 22' 


23° 27^' 


23 '20° 7' 




4' S 


23 3 27 


25 19° 41' 


10° 48' 




50' 


12° 6' 


20° 46' 


23° 25' 


27 19° 15' 


10° 6' 


1° 


37' 


12° 48' 


21° 9' 


23 } 21' 


29jl8° 47' 


9° 23' 


2° 


24' 


13° 28' 


21° 30' 


23° 15' 



Declination in the heavens is the same as latitude on the 
earth. When the sun is on the meridian of Greenwich, in 
1858, the preceding table of declination shows in what latitude 
the sun will be in the zenith at noon. 



198 SEQUEL. 

This table also enables us to solve all problems like the fol- 
lowing, with or without the use of the globes. 

1 . On the 3d day of July, where on the earth will the sun be verti- 
cal (or nearly so), when it is 3 P. M., apparent time, at Xew York? 

The longitude of New York is 74° west, and when the sun 
is on the meridian of New York, it is then apparent noon. 
Three hours afterwards, the sun will be on the meridian, which 
is 45° west of New York, or in the longitude 119° west. 

The sun passes the meridian of Greenwich in lat. 22° 59' 
north, and the variation for one day, or 360° of longitude is 5', 
therefore, the variation for 119° is 1* 40" nearly. 

Whence, when it is 3 P. M. at New York, the sun is vertical 
over that point, on the earth, whose lat. is 22° 57' 20" north, 
and Ion. 119° west. 

2. On the 27th day of February, 1858, at 9h. 12m. P. M., 
apparent time at Greenwich, the sun and moon will be in oppo- 
sition, * at which tine there will be an eclipse of the moon. Deter- 
mine, by the globe, where the eclipse will be visible. 

When it is 9h. 12m. at Greenwich, the sun is on the meri- 
dian 138° west, (computing 15° to each hour,) and the moon 
is 180° from that, counting either way. Therefore the moon 
must be on the meridian in longitude 42° east. 

The declination of the sun at that time will be 8° IT 14" S. 

The declination of the moon, - - - 9° 5' 3" N. 

The one is not exactly opposite to the other in declination, 
therefore the moon will not pass through the center of the 
earth's shadow, but 53' 49" north of that center, making a par- 
tial eclipse on the moon's southern limb. 

The moon will be in the zenith of lat. 9° 7' north, and Ion. 
42° east. Find that point on the globe ; it lies in upper Egypt. 

That point is the pole of the visible eclipse, — that is, the 
visibility will extend over all places within 90° of that point. 
Hence, it will be visible from all parts of Africa, Europe, Asia 

• This was written in 1857, therefore in the future tense. 



PROBLEMS ON THE GLOBES. 199 

as far as Japan, and the western part of New Holland. It will 
be visible in the eastern part of Brazil, and invisible to all 
western America and the Pacific ocean. 

3. July 23o?, 1888, at 6k. A. M., apparent time at Greenwich, 
the sun and moon will come in opposition, and there will be an 
eclipse of the moon. Where will that eclipse be visible, or where 
will the moon be nearly vertical? 

Ans. The moon will be nearly vertical in lat. 20° 16' south, 
and in longitude 90° west. 

And this point is the pole of visibility. Hence, the eclipse 
will be visible to all South and North America to lat. 70° north, 
and invisible in the opposite hemisphere. 

4. What other day of the year has the same length as the 5th 
of May? Ans. August 7th. 

On the 5th of May, the sun's declination is 16° 15' N., and 
by inspecting the table, we find nearly the same declination on 
the 7th of August. 

5. What other day of the year has the same length as the 1st 
day of March? Ans. October 13th. 

Problem 8. Given the meridian altitude of the sun, and the 
sun's declination at the same time, to determine the latitude. 

Solved with or without a globe, first with a globe. Suppose 
the latitude to be north. 

Rule. — Take that part of the brass meridian which is numbered from 
the equator to the poles ; and take the degree on that meridian corres- 
ponding to the sun's declination, north or south, as the case may be. Turn 
the meridian, or so adjust it, that the given point of declination, shall cor- 
respond to the given meridian altitude of the sun. 

Then the elevation of the pole above the horizon will be the latitude 
required. 

EXAMPLE. 

1. Suppose the sun's declination was 20° JV1, and the sun's 
true meridian altitude at the same time, ivas 70° from the southern 
horizon. What zoas the latitude? Ans. 40° N. 



200 SEQUEL. 

I place the 20th degree of north declination 70 degrees from 
the southern horizon. The equator then is 50° above the hori- 
zon, and consequently the southern pole must be 40° below 
the southern horizon, and the northern pole 40° above the 
northern horizon, or the latitude is 40° K". 

Without a globe, the latitude is computed by the following 
formula : 

(90°— A)±D=Lat. 

In this equation, A represents the observed meridian altitude 
corrected for refraction, semi-diameter, and index error, if any. 
D is the declination computed to the precise time of observa- 
tion, (90° — A), is the meridian zenith distance, and if we 
represent it by Z, the formula becomes 
Z±D=Lat. 

The plus sign is used when the declination is north, and the 
minus sign when it is south. Z is minus when the meridian 
altitude is measured from the northern horizon — and in all 
cases when the result is minus, the latitude is south. 

EXAMPLES. 

1. The true meridian altitude of the sun was 27° 32', measured 
from the southern horizon, when its declination was 6° 43' north. 

What was the lalitude? Ans. 69° 1 1' north. 

2. The true meridian altitude of the sun was 76° 10' from the 
south, when the sun's declination was 21° 2' north. What tvas the 
latitude? Ans. 34° 52' north. 

3. The true meridian altitude of the sun was 13° 18' from the 
south, when the sun's declination was 19° 47' south. What was the 
latitude? Ans. 56° 55' north. 

4. The true meridian altitude of the sun was 76° 17' from the 
northern horizon, when the sun's declination was 23° 4' north. 

What was the latitude? Ans. 9° 21' north. 

N. B. In all the preceding examples D is plus. In the 
4th example, Z is 13° 43' minus. 



PROBLEMS OK THE GLOBES. 201 

5. The true meridian altitude of ike sun was 53° 10' from the 
north, when the sun's declination was 23° 4' north. What was the 
latitude? Aus. 12° 48' south. 

6. The true meridian altitude of the sun was 68° 20' from the 
north, when the sun's declination ivas 22° 10' south. What was the 
latitude? Ans. 30' south. 

7. The true meridian altitude of the sun was 57° 35' from the 
south, when the sun's declination ivas 22° 10' south. What was 
the latitude? Ans. 10° 15' north. 

Thus we might give examples without end, but we think 
that we have sufficiently illustrated the principle of finding 
latitude by meridian altitudes. 

No matter what heavenly body is used, moon, star, or planet, 
provided the declination of the object used is known, and the 
observer can see the horizon. Stars are rarely used for this 
purpose, because the horizon can rarely be seen at sea when 
the stars are visible. 

If the object be the moon, its parallax in altitude must be 
taken into the account ; hence, that body is seldom used by the 
common navigator, and the unscientific observer. 

In observatories, zenith distances can be directly observed. 
Observers there, do not depend on the horizon. 

We give a few examples of finding the latitude by the meri- 
dian zenith distances of some of the stars. 

8. The fixed star Spica, was observed to pass the meridian of 
one observer 21° 3' from the zenith towards the south : to another 
observer it passed the meridian 13° AY from the zenith towards the 
north. What was the latitude of each observer? 

Ans. Lat. of one, 10° 42' N.; of the other, 34° 2' S. 
(N. B. For the declination of the stars, see Table II.) 

9. The fixed star Castor, was observed to pass the meridian 12° 
13' to the north of the zenith. What ivas the latitude? 

Ans. 20° north. 



202 SEQUEL. 

10. Suppose the meridian distance had been the same toward 
the south, what would have been the latitude? 

Ans. 44° 46' north. 

11. The star a, in Cassiopea, whose right ascension is 31m. 495. 
and declination 55° 42' north, was observed to pass the meridian 
[below the pole) 64° 20' from the zenith. What was the latitude? 

Ans. 59° 58' north. 

12. Had the zenith distance been the same when the star was 
above the pole, measured towards the north, what then would have 
been the latitude? Ans. 8° 38' south. 



PROBLEMS ON THE CELESTIAL GLOBE. 

Problem 1. To find the natural appearance of the heavens as 
seen from any given latitude at any given hour on any given day. 

Rule. — Elevate or depress the north pole to correspond to the given lat- 
itude. Find the sun's place in the ecliptic for the given day, and bring 
that point to the brass meridian. Set the index at 12. Then turn the globe 
to correspond to the given hour. (Turn westward if the given hour is 
after noon — and eastward if before noon.) 

The position of the jlobe will now represent the true position of the heavens. 

Those stars that are near the brass meridian on the globe, will be found 
to be near the meridian in the heavens — and those stars that are near the 
eastern horizon on the globe, will be found to be near the eastern horizon 
in the heavens, <fec. &c. 

EXAMPLES. 

1. At London, lat. 51° 30' N. at 2 A. M. on the 20th day of 
January, what stars are rising, what stars are setting, and what 
stars are on the meridian? 

Ans. Lyra and Spica are rising, Regulus is near the meri- 
dian, and all stars near the western horizon, on the 
globe, are setting. 

2. Find the position of the stars to an observer in 40° of north 
latitude, on the 1th of November, at 10 o'clock in the evening, appa- 
rent time. Ans. The R. A. of the meridian is 51m. 



PROBLEMS ON THE GLOBES. 203 

That is, whatever stars, or planets have the right ascension of 
51 minutes, are near the meridian, at that time. As the right 
ascension of Aldebaran is 4h. 27m., therefore Aldebaran is 3h. 
36m. east of the meridian, or Aldebaran will be on the meridian 
at 1.36 A. M. on the 8th of November. 

The position of the globe shows the true position of the stars. 

N. B. Find the sun's right ascension for the given time, 
and adS the given hour to it. Subtracting 24h. if the sum ex- 
ceeds 24. Thus, on the 7th of November, the right ascension 
of the sun is 14h. 51m., adding lOh. and rejecting 24h., pro- 
duces 51 minutes. 

3. Wliat stars never set in latitude 40° north? 
Ans. All stars, within 40 degrees of the north pole; and the 
same is true for any other latitude. 

Problem 2. To find the position of any particular star in 
reference to the meridian, on any given day, at any given hour of 
that day, by the globe. The latitude may, or may not, be given. 

Rule. — Find the sun's postion on the globe by its place in the ecliptic 
on the given day, or find its right ascension and declination, and bring 
that point to the brass meridian. That is the position of the globe at noon. 
Set the index at 12, and turn the globe east or west, to correspond to the 
given hour of the day. Then look for the star, and wherever it be found 
on the globe, the corresponding point in the heavens will be its place. And 
if the globe be placed where a fair view of the heavens can be had, and 
the brass meridian placed north and south, and the pole elevated to cor- 
respond with the latitude of the place, then a line from the center of the 
globe through the star, on the globe, continued to the heavens, will point 
out the star, or pass very near it. 

WITHOUT THE GLOBE. 

Rule. — Subtract the right ascension of the sun from the right ascension 
of the star, and the remainder is the apparent time when the star comes to 
the meridian. This time, compared with the given time, will determine 
whether the star is east or west of the meridian, and how far. 

EXAMPLES. 

1. On the \0th of January, what is the position of the dog star 
Sirius, at 9 P, M., apparent time? 

Ans. 2h. 14m. east of the meridian. 



204 SEQUEL. 

N. B. On the 10th of January, at 9 P. M., the right ascension of the sun 
is never far from 19h. 25m., and the right ascension of Sirius is 6h. 39m. 
Whence 24+(6+39), or 30h. 39m.— 19h. 25m. — llh. 14m. That is, on 
that day of the year, Sirius comes to the meridian not far from 14m. past 
eleven, apparent time ; therefore, at 9 P. M. it must be 2h. and 14m. east of 
the meridian — whatever be the latitude of the observer. 

2. What is the position of Antares at 10 P. M. on the 4th of 
July? Arts. It is 35m. west of the meridian. 

Remark. — "We find the time when the moon or a planet will pass the 
meridian, on the same principle as we find the time for a star, except that 
we must be more particular — as the right ascensions of the moon and 
planets change, and the stars are supposed to be fixed. 

"We must have the right ascension of sun and planet at the exact time 
when the planet passes the meridian. 

But we can illustrate more clearly by the following example : 

On the 5th of August, at noon, Greenwich time, the right ascen- 
sion of the sun was, by the Nautical Almanac, 9h. 2m. 355.56, 
and the hourly variation was 9s. 59. 

The right ascension of the moon, at the same time, was 12A. 19m. 
385.2, and the hourly increase was \m. 445.4. At what time did 
the moon pass the meridian of 75° ivest longitude, on that day? 

h. m. 8. 
From Q) right ascension, 

Subt. ^ right ascension, 

Appro.v. time Q) passes Gr. 

Add for Lon. 75° W. 

Correction to be made for 
Q) R. A. increases, per hour, 1m. 
^ R. A. increases, per hour, 

Variation per hour, - lm. 34s. 81 and this for 8}£h. 

gives a variation of 13m. 5s. 28. 

h. m. s. 
Whence, to the approx. time at Gr. 3 17 2.84 

Add 13 5.28 

Q) passes merid. in Lon. 75° W. at 3 30 8.12 app. time.* 

Equation of time, add - - 5 40 

Q) passes merid. of Lon. 75° W. at 3 35 48 mean time. 

* To be perfectly accurate, we should correct for 8h. 30m. 8s., or correct 
twice 



- 


12 19 38.20 


- 


9 2 35.36 


- 


3 17 2.84 


- 


5 


- 


- 8 17 2 


44s.4 




9s.59 





PROBLEMS ON THE GLOBES. 



205 



Problem 3. To find the time, on any particular day, when 
any heavenly body, whose declination is given, will rise and set. 

We must first find the time that the given body passes the meridian, as 
taught in the foregoing examples. Then we must obtain the semi-diurnal 
arc, which is the time required for a body to pass from the horizon to the 
meridian, or from the meridian to the horizon, and this interval depends on 
the declination of the body, and the latitude of the place from which it is 
observed. 

When the declination of a body is zero, that is, on the celestial equator, 
the semi-diurnal arc is six hours, observed from all localities. 

"When the latitude and declination are both north, or both south, that 
interval is greater than six hours. 

When the latitude and declination are on opposite sides of the equator, 
the semi-diurnal arc is always less than six hours. 

The difference between six hours and the semi-diurnal arc is 
called Ascensional Difference, and its values will be found in 
the following table, corresponding to various declinations, from 
1° to 27°. Under the declination, and opposite the latitude, 
will be found the corresponding ascensional difference. 

For a practical work, a more complete table would be given. 











Delination 


of Ip, Q), -^-, or Planet. 






Lat. 


1 


3 Q 


6° 


9 Q 


10° 


12° 


14° 


16° 


18^ 


20° 


22° 


23* 


24° 


25° 


26° 


27* 




m 


Wl 


m 


m 


m 


m 


m 


m 


m 


wi 


Wl 


m 


m 


m 


m 


m 


18 


1 


4 


8 


12 


13 


16 


19 


21 


29 


27 


40 


32 


33 


35 


36 


38 


21 


2 


5 


9 


14 


.16 


19 


22 


25 


33 


32 


96 


38 


39 


41 


43 


45 


24 


2 


5 


1116 


18 


22 


26 


29 


39 


37 


41 


44 


46 


68 


50 


52 


27 


2 


6 


1219 


21 


25 


29 


34 


43 


43 


48 


50 


52 


53 


58 


50 








i 
I 


















h \h 


k 


h 


30 


2 


7 


1421 


23 


28 


33 


38 


49 


49 


54 
h 
1 1 


57 

h 
1 4 


1 01 21 51 8 

i 


33 


3 


8 


1624 


26 


32 


37 


43 


55 


55 
h 
1 1 


1 71 111 14 


1 17 


36 


3 


9 


48,26 


29 


36 


42 


48 


h 
1 1 


I 8 


1 12 


1 161 191 23 


1 27 


39 


3 


10 


20 29 


33 


40 


47 


54 
k 
1 


1 9 


1 16 


1 20 


1 251 2911 33 

1 


1 37 


42 


4 


11 


22 33 


37 


44 


52 


1 8 


1 17 


1 25 


1 30 


1 351 391 441 48 


45 


412 


24^9 


41 


49 


58 
h 
1 4 


1 7 


1 16 


1 25 


1 35 1 40 

| 


1 461 511 57 2 3 

i 


48 


L 


2844 


45 


55 

1 i 


1 14 


1 25 


1 35 


1 471 53 


1 59 2 5 2 11 2 28 

| 


51 


5 


14 


30'45 


50 


7 12 


1 23 


1 35 


1 47 


2 02 6 


2 13 2 212 24'2 36 


52 


5 


15 


3147 


52 


1 3 


1 14 


1 26 


t 38 


I 51 


2 52 122 19 2 27 2 35,2 43 


53 


516 


32 49 


54 


1 6 


1 17 


1 29 


1 42 


I 56 


2 10 2 17 2 25 2 33 2 49 2 5S 


54 


617 


33 50 


56 


1 8 


1 20 


1 33 


] 46 2 


2 15 2 232 31 2 40 2 5713 7 



206 SEQUEL. 

EXAMPLES. 

1. On the \0th day of January, 1858, the right ascensisn of 

the planet Jupiter loill be 2A. 16m. 52*., and decimation 12° 32' 

north. The right ascension of the sun, at the same time, will be 

19A. 28m. nearly. What time will the planet pass the meridian, 

and what time will it rise and set, observed from latitude 42° north? 

h. m. s. 
From the R. A. of Jupiter, +24h. 26 16 52 

Subt. the R. A. of sun, - - 19 28 

Apparent time that Jupiter passes mer. 
To 6h. add Ascensional diff. 45m. 



6 


48 


52 


P. 


M. 


6 


45 




P. 






3 


52 


M. 


1 


33 


52 


A, 


, M. 



Jupiter rises, (apparent time,) 
Jupiter sets, (next morning,) at 

2. What time (approximately) will Sirius rise, pass the mer* 
dian, and set, on 4th of March, observed from New York? 

h. m. 
FromR. A. Sirius +24h. (see Tab. II,) 30 39 nearly. 

Subt. R. A. of sun, (see p. 6, of Tables) 23 1 nearly. 



Sirius passes meridian, apparent time, 7 38 P. M. 

From 6h. take lh. nearly, (semi-diur. arc,) 5 

Sirius rises at - - - - 2 38 P. M. 

Sirius sets next morning at - - 38 A. M. 

Thus we might operate with any planet, or star. 

The moon requires more care ; we must have its right as- 
cension and declination, at times, as near that of rising and 
setting, as we can procure, and also, take parallax into account. 



TABLES. 

EXTRACTS FROM THE NAUTICAL ALMANAC FOR JANUARY, 1846. 



J 

c 

I 

a 


THE SUN'S 
Apparent 


LogaT. 
of the 
Radius 
Vector 
of the 
Earth. 


THE MOON'S 


Longitude. 


Latitude. 


Longitude. 


Latitude. 


Semi- 
diam. 


Hor. 
Paral. 


Noon. 


Noon. 


Noon. 


Noon. 


Noon. 


Noon. 


Noon. 


o / // 


// 




o // 


o / // 


/ // 


/ n 


1 
2 
3 


280 46 15.3 

281 47 26.1 

282 48 36.5 


N.0.49 
0.45 
0.37 


9.99266 
9.99266 
9.99267 


330 42 13.9 
345 7 12.0 
359 4 55.4 


N.4 54 8.5 
4 24 8.7 
3 39 5.9 


16 21.6 
16 8.3 
15 53.9 


60 2.3 
59 13.5 
58 20.5 


4 

5 
6 


283 49 46.5 

284 50 56.1 

285 52 5.3 


0.27 

0.16 

N.0.03 


9.99267 
9.99268 
9.99268 


12 35 34.7 
25 41 31.5 
38 26 25.0 


2 43 1.9 

1 39 55.7 
N.O 33 28.3 


15 39.8 
15 26.7 
15 15.2 


57 28.7 
56 40.8 
55 58.7 


7 
8 
9 


286 53 13.9 

287 54 22.0 

288 55 29.7 


S.0.11 
0.25 
0.38 


9.99270 
9.99271 
9.99272 


50 54 23.2 
63 9 30.1 
75 15 21.8 


S.O 33 3 6 

1 36 46.8 

2 35 8.6 


15 5.6 
14 57.6 
14 51.5 


55 23.3 
54 54.1 
54 31.6 


10 
11 
12 


289 56 36.8 

290 57 43.4 

291 58 49-5 


0.49 
0.58 
0.65 


9.99274 
9.99277 
9.99279 


87 14 56.3 

99 10 31.3 

111 3 50.8 


3 25 55.4 

4 7 13.7 
4 37 30.7 


14 46.9 
14 43.8 
14 42.1 


54 14.6 
54 3.3 
53 57.0 


13 
14 
15 


292 59 55.3 

294 1 0.5 

295 2 5.4 


0.70 
0.71 
0.69 


9.99282 
9.99285 
9.9928? 


122 56 17.6 
134 49 7.9 
146 43 48.4 


4 55 38.9 

5 56.4 
4 53 7.6 


14 41.7 
14 42.8 
14 45.5 


53 55.7 

53 59.8 

54 9.7 


16 
17 

18 


296 3 9.9 

297 4 14.0 

298 5 17.8 


0.64 
0.57 
0.47 


9.99292 
9.99295 
9.99299 


158 42 11.3 

170 46 44.8 
183 38.7 


4 32 23.1 
3 59 17.1 
3 14 47.1 


14 50.0 

14 56.3 

15 4.6 


54 26.0 

54 49.0 

55 19.7 


19 

20 
21 


299 6 21.2 

300 7 24.2 

301 8 26.7 


0.35 

0.23 

S. 0.09 


9.99304 
9.99308 
9.99313 


195 27 41.8 
208 12 10.4 
221 18 27 5 


2 20 14.2 

1 17 27.8 

S.O 8 53.1 


15 15.2 

15 27.7 
15 42.0 


55 58.4 

56 44.4 

57 37.0 


22 
23 
24 


302 9 28.9 

303 10 30.4 

304 11 31.3 


N.0.04 
0.15 
0.25 


9.99318 
9.99323 
9.99328 


234 50 26.7 
248 50 42.5 
263 19 30.4 


N.l 2 20.5 

2 12 11.7 

3 15 50.9 


15 57.3 

16 12.5 
16 26.2 


58 32.9 

59 28.8 

60 19.0 


25 
26 

27 


305 12 31.5 
3Ub 13 30.9 
307 14 29.3 


0.33 
0.38 
0.40 


9.99334 
9.99339 
9.99345 


278 13 48.8 
293 26 49.2 
308 48 22.8 


4 8 2.8 
4 43 49.4 
4 59 32.4 


16 36.8 
16 42.9 
16 43.5 


60 57.9 

61 20.2 
61 22.6 


28 
29 
30 
31 


308 15 26.8 

309 16 23.3 

310 17 18.5 

311 18 12.6 


0.40 
0.37 
0.30 
0.21 


9.99351 
9.99357 
9.99363 
9.99369 


324 6 34.0 

339 9 55.3 

353 49 32.0 

8 13.1 


4 53 45.4 
4 27 32.9 
3 44 8.2 

2 47 58.7 


16 38.7 
16 2W.9 
16 15.6 
16 0.2 


61 4.9 
60 29.1 
59 40.2 
53 43.7 


32 


312 19 5.3 


N.0.10 


9.99375 


21 40 34.3 


N.l 43 50.6 


15 44.2 


57 45.1 



TABLES. 



TABLE I. 

MEAN ASTRONOMICAL REFRACTIONS. 
Barometer 30 in. Thermometer, Fah. 50°. 



Ap. Alt. 
W 0' 


Refr. 


Ap. Alt. 


Reir. 


Ap. Alt. 


Refr. 


Alt. 


Refr. 


33' 51" 


4* 0' 


11' 52" 


12° 0' 


4' 28.1" 


42° 


1 4.6' 


5 


32 53 


10 


11 30 


10 


4 24.4 


43 


1 2.4 


10 


31 58 


20 


11 10 


20 


4 20.8 


44 


1 0.3 


15 


31 5 


30 


10 50 


30 


4 17.3 


45 


58.1 


20 


30 13 


40 


10 32 


40 


4 13.9 


46 


56.1 


25 


29 24 


50 


10 15 


50 


4 10.7 


47 


54.2 


30 


28 37 


5 


9 58 


13 


4 7.5 


48 


52.3 


35 


27 51 


10 


9 42 


10 


4 4.4 


49 


50.5 


40 


27 6 


20 


9 27 


20 


4 14 


50 


48.8 


45 


26 24 


30 


9 11 


SO 


3 58.4 


51 


47.1 


50 


25 43 


40 


8 58 


40 


3 55.5 


52 


45.4 


55 


25 3 


50 


8 45 


50 


3 52.6 


53 


43.8 


1 


24 25 


6 


8 32 


14 


3 49.9 


54 


42.2 


5 


23 48 


10 


8 20 


10 


3 47.1 


55 


40.8 


10 


23 13 


20 


8 9 


20 


3 44.4- 


56 


39.3 


15 


22 40 


30 


7 58 


30 


3 41.8 


57 


37.8 


20 


22 8 


40 


7 47 


40 


3 39.2 


58 


36.4 


25 


21 37 


50 


7 37 


50 


3 36.7 


59 


35.0 


30 


21 7 


7 


7 27 


15 O 


3 34.3 


60 


33.6 


35 


20 38 


10 


7 17 


15 30 


3 27.3 


61 


32.3 


40 


20 10 


20 


7 8 


16 


3 20.6 


62 


31.0 


45 


19 43 


30 


6 59 


16 30 


3 14.4 


63 


29.7 


50 


19 17 


40 


6 51 


17 


3 8.5 


64 


28.4 


55 


18 52 


50 


6 43 


17 30 


3 2.9 


65 


27.2 


2 


18 29 


8 


6 35 


13 


2 57.6 


66 


25.9 


5 


18 5 


10 


6 28 


19 


2 47.7 


67 


24.7 


10 


17 43 


20 


6 21 


20 


2 38.7 


68 


25.5 


15 


17 21 


30 


6 14 


21 


2 30.5 


69 


22.4 


20 


17 


40 


6 7 


22 


2 23.2 


70 


21.2 


25 


16 40 


50 


6 


23 


2 16.5 


71 


19.9 


30 


16 21 


9 


5 54 


24 


2 10.1 


72 


18.8 


35 


16 2 


10 


5 47 


25 


2 4.2 


73 


17.7 


40 


15 43 


20 


5 41 


26 


1 58.8 


74 


16.6 


45 


15 25 


30 


5 36 


27 


1 53.8 


75 


15.5 


50 


15 8 


40 


5 30 


28 


1 49.1 


76 


14.4 


55 


14 51 


50 


5 25 


29 


1 44.7 


77 


13.4 


3 


14 35 


10 


5 20 


30 


1 40.5 


78 


12.3 


5 


14 19 


10 


5 15 


31 


1 36.6 


79 


11.2 


10 


14 4 


20 


5 10 


32 


1 33.0 


80 


10.2 


15 


13 50 


30 


5 5 


33 


1 29.5 


81 


9.2 


20 


13 35 


40 


5 


34 


1 26.1 


82 


8.2 


25 


13 21 


50 


4 56 


35 


1 23.0 


83 


7.1 


30 


13 7 


11 


4 51 


36 


1 20.0 


84 


6.1 


35 


12 53 


10 


4 47 


37 


1 17.1 


85 


5.1 


40 


12 41 


20 


4 43 


38 


1 14.4 


86 


4.1 


45 


12 28 


30 


4 39 


39 


1 11.8 


87 


3.1 


50 


12 16 


40 


4 35 


40 


1 9.3 


88 


2.0 


55 


12 3 


SO 


4 31 


41 


i s:9 


89 


1-0 



TABLE C. 

CORRECTION OF MEAN REFRACTION. 

Hight of the Thermometer. 



App. 

Alt. 
o ' 


24c 


28< 


> 32° 


36° 


40° 


440 


52° 


56° 


60° 


64° 


68° 


72< 


> 76c 


86° 


'+' 


'+' 


'+" 


'+" 


'+" 


'-+-" 


'__" 


'_" 


'_" 


'_" 


— " 


'__' 


'__' 


'— " 


0.10 


2.18 


1.55 


1.33 


1.11 


51 


31 


10 


29 


48 


1.07 


1.25 


1.43 


2.01 


2.19 


0.00 


2.12 


1.49 


1.28 


1.08 


48 


29 


9 


27 


45 


1.04 


1.21 


1.36 


1.54 


2.12 


0.20 


2.05 


1.44 


1.24 


1.04 


46 


28 


9 


26 


44 


1.01 


1.17 


1.33 


1.49 


2.05 


0.30 


1.59 


1.39 


1.20 


1.01 


44 


26 


8 


25 


41 


58 


1.13 


1.28 


1.43 


1.59 


0.40 


1.53 


1.34 


1.16 


58 


42 


25 


8 


24 


39 


55 


1.10 


1.24 


1.38 


1.53 


0.50 


1.48 


1.29 


1.12 


55 


40 


24 


8 


23 


37 


52 


1.06 


1.20 


1.34 


1.48 


1.00 


1.43 


1.25 


1.09 


53 


38 


23 


7 


21 


36 


50 


1.03 


1.17 


1.30 


1.43 


1.10 


1.38 


1.21 


1.06 


50 


36 


22 


7 


20 


34 


48 


1.00 


1.13 


1.26 


1.38 


1.20 


1.33 


1.17 


1.03 


48 


34 


21 


6 


19 


32 


45 


57 


1.09 


1.21 


1.33 


1.30 


1.29 


1.14 


1.00 


46 


32 


20 


6 


18 


31 


43 


54 


1.06 


1.18 


1.29 


1.40 


1.25 


1.11 


57 


44 


31 


18 


6 


18 


30 


41 


52 


1.04 


1.15 


1.25 


1.50 


1.21 


1.08 


55 


42 


30 


17 


6 


17 


28 


39 


50 


1.01 


1.11 


1.21 


2.00 


1.18 


1.05 


53 


39 


29 


17 


5 


16 


27 


37 


48 


58 


1.08 


1.18 


2.20 


1.11 


1.00 


48 


37 


26 


16 


5 


15 


25 


35 


44 


54 


1.03 


1.11 


2.40 


1.06 


55 


44 


34 


24 


14 


5 


14 


23 


32 


41 


50 


58 


1.06 


3.00 


1.01 


51 


41 


32 


22 


13 


4 


13 


21 


30 


38 


46 


54 


1.01 


3.20 


57 


47 


38 


29 


21 


13 


4 


12 


20 


28 


35 


43 


50 


57 


3.40 


53 


44 


36 


28 


20 


12 


4 


11 


18 


26 


33 


40 


47 


53 


4.00 


49 


41 


33 


26 


18 


11 


4 


10 


17 


24 


31 


37 


44 


50 


4.30 


45 


38 


31 


24 


17 


10 


3 


9 


16 


22 


28 


34 


40 


45 


5.00 


41 


35 


28 


22 


16 


9 


3 


9 


14 


20 


26 


31 


36 


40 


5.30 


38 


32 


26 


20 


14 


9 


3 


8 


13 


19 


24 


29 


34 


38 


6.00 


35 


30 


24 


19 


13 


8 


2 


7 


12 


17 


22 


26 


31 


35 


6.30 


33 


28 


22 


17 


12 


7 


2 


7 


11 


15 


20 


24 


29 


33 


7.00 


31 


26 


21 


16 


12 


7 


2 


6 


10 


14 


19 


23 


27 


3l! 


8 


27 


23 


19 


15 


10 


6 


2 


5 


9 


13 


16 


20 


24 


27 


9 


24 


20 


16 


13 


9 


5 


2 


5 


8 


11 


14 


18 


21 


24 


10 


22 


18 


15 


12 


8 


5 




4 


7 


10 


13 


16 


19 


22 


11 


20 


17 


14 


11 


8 


5 




4 


7 


9 


12 


15 


18 


20 


12 


18 


15 


13 


10 


7 


4 




4 


6 


9 


11 


13 


16 


18 


13 


17 


14 


12 


9 


7 


4 




3 


6 


8 


10 


12 


15 


17 


14 


16 


13 


11 


8 


6 


4 




3 


5 


7 


9 


11 


14 


16 


15 


15 


12 


10 


8 


6 


3 




3 


5 


7 


9 


11 


13 


15 


16 


14 


12 


9 


7 


5 


3 




3 


5 


6 


8 


10 


12 


14 


17 


13 


11 


9 


7 


5 


3 




3 


4 


6 


8 


9 


11 


13 


18 


12 


10 


8 


6 


5 


3 




2 


4 


6 


7 


9 


10 


12 


19 


11 


9 


8 


6 


4 


3 




2 


4 


5 


7 


8 


10 


11 


20 


11 


9 


7 


6 


4 


2 




2 


4 


5 


6 


8 


9 


11 


21 


10 


9 


7 


5 


4 


2 




2 


3 


5 


6 


7 


9 


10 


22 


10 


8 


7 


5 


4 


2 




2 


3 


5 


6 


7 


8 


10 


23 


9 


8 


6 


5 


4 


2 




2 


3 


4 


6 


7 


8 


9 


24 


9 


7 


6 


5 


3 


2 




2 


3 


4 


5 


6 


8 


9 


25 


8 


7 


6 


5 


3 


2 




2 


3 


4 


5 


6 


7 


8 


26 


8 


7 


6 


4 


3 


2 




2 


3 


4 


5 


6 


7 


8 


27 


8 


6 


5 


4 


3 


2 




2 


3 


4 


5 


6 


7 


8 


28 


7 


6 


5 


4 


3 


2 





1 


2 


3 


5 


5 


6 




30 


7 


6 


5 


4 


3 


2 





1 


2 


3 


4 


5 


6 


7 






— 


— 


— 


— 


H- 


+ 


~h 


+ 


4- 








28.261 


28.56] 


28.85 i 


2915 


29.75 : 


10.05 ; 


t0.35 . 


50.64 : 


10.93 










Higl 


it of t 


hcBa 


romel 


er. 









TABLES. 
TABLE II. 

MEAN PLACES FOR 100 PRINCIPAL FIXED STABS, FOR JAN. 1, 1846, 



Star's Name. 



a Andromeda,. . . . 
y Pegasi (Algenib), 

Hydri, , 

a Cassiope^e, 



£ Oeti, 

a Urs. Min. (Polaris),. 

6 l Geti, 

a Eridani (Achernar),. 



A ARIETIS,. 

y Ceti, 

a Csrr,.. . . 

a Persei, .. 



n Tauri, 

y* Eridani, 

et Tauei, (Aldebaran) , 

a Auriga, (Capella),. 

$ Orionis, (Riyel), . . 

Tauri, 

cT Orionis, 

a Lepris, 



i Orionis, . ... 
a Columbae, . 
a Orionis, .. . . 
y. Geminorum, 



Argus, (Canopus) , . . . 

51 (Hev.) Cephei, 

t Canis Maj., (Sinus)) 
t Canis Majoris, 



S Geminorum, 

a 2 Geminor. (Castor),.. . 
a Can. Min., (Procyon), 
fi Geminor, (Pollux),.. 

15 Argus, 

i Hydrse, 

i Ursae Majoris, 

t Argus, 

A HYDRiE, 

9 Ursae Majoris, 

» Leonis,.. 

* Leonib, (Regulus),. . . 



1 

2.3 

3 

3 

2.3 
2.3 

3 

1 

3 

3 
2.3 
2.3 

3 

2.3 
1 
1 

1 
2 
2 

3.4 

2.3 
2 
1 
3 

1 

6 
1 

2.3 

3.4 
3 

1 .2 
2 

3.4 

4 

3.4 

2 

2 
3 
3 

1 



Right Ascen, 



Annual Yar 



26.257 
5 18.691 
17 34.168 
31 48.294 

35 51.339 

1 3 52.226 
1 16 19.692 
1 31 58.291 

1 58 30.193 

2 35 19.633 

2 54 14.072 

3 13 21.403 

3 38 20.382 

3 50 50.760 

4 27 5.404 

5 5 19.317 

5 7 8.383 

5 16 33.662 

5 24 8.428 

5 25 56.406 



3.0720 
3.0784 
3.3054* 
3.3418 

-4- 2.9995 
17.1346* 
3.0015 
2.2339 

+ 3.3475 
3.1085 
3.1266 
4.2324 

+ 3.5473 

2.7898 
3.4274 
4.4082 

+ 2.8787 
3.7827 
3.0609 
2.6425 



5 28 24.062 + 3.0404 

5 34 4 531 2.1691 

5 46 50.189! 3.2433 

6 13 38.621 1 3.6257 

6 20 32.145!+ 1.3279 
6 26 30.2871 30.7946 
6 38 21.883 2.6459* 
6 52 34.440 2.3558 



7 10 55.298 
7 24 46.065 
7 31 14.237 
7 35 53.153 



-}- 3.5918 
3.8561 
3.1445* 
3.6829* 



8 59.232'+ 2.5596 

8 38 37.154! 3.1966 

8 48 38.088 4.1261* 

9 12 58.192 1.6100 



9 20 1.170 

9 22 31.453 

9 37 6.098 

10 10.062 



2.9499 
4.0504' 
3.4258 
3.2211 



Declination. 



deg. min. sec. 

N.28 14 25.40 
NU4 19 37.80 
S.78 7 24.40 
N.55 41 31.08 

S.18 49 59.01 

N.88 29 17.88 

S. 8 58 45 93 

58 1 14.34 



Ann. Var. 



+20.055 
20.050 
19.997 
19.862 

+19.810 
19.279 
18.952 
18.461 



N.22 43 53.86J+1 7.432 
N". 2 35 1.17 15.621 
N. 3 28 55 70 14.532 
N.49 18 28.20 13.329 

N.23 37 27.73+11.620 
S. 13 57 1.50 10.711 
N.16 11 41.39 7.097 
N".45 50 6.56 4.737 

S. 8 23 3.33!+ 4.583 



N\28 28 17.49 
S. 25 4.86 
S. 17 56 12.77 

S. 1 18 17.53 

S.34 9 36.95 

N". 7 22 22.32 

N.22 35 13.16 

S.52 36 49.17 
N.87 15 31.20 
S. 16 30 32.83 
S.28 45 59.38 

N".22 15 37.4 
N.32 13 12.93 
N. 5 36 54.95 
IST.28 23 34.06 

S.23 51 50.94 

N. 6 58 48.51 
N.48 38 32.35 
S.58 37 49.78 

5. 7 59 39.05 
N.52 22 31.09 
N.24 28 49.46 
X.12 43 2.96 



3.776 
3.123 

2.968 

+ 2.754 

2.262 

+ 1.149 

— 1.196 

— 1.796 
2.337 

4.484* 
4.562 

— 6.110 
7.253 

8.758* 
8.152 

-10.104 
12.800 
13.464 
]4.96i 

—15.366 
16.108* 
16.283 

-17.377 



TABLE II. 



Star's Name. 



n Argus, 

* Urs^ Majoeis,.. . . 

i Leo.nis, 

<f Hydrse et Crateris, 



Leonis, 

y Ursje Majoeis, 
Chamasleontis, 
* l Cracis , 



Corvi, 

12 Camim Venaticorum 

a. Vieginis, (Spica,) 

» Urs^e Majoeis, 



x Bootis, , 

Oentauri, 

* Boons, (Arcinrus,) 
a 2 Centauri, , 



s Boons, 

*2 Librae, 

Uksjs Minoeis,. 
& Libras, 



a CORONJE BOEEALIS,.. 

a Seepentis, 

£ Ursse Minoris, 

/3 1 Scorpii, 



S Ophiuchi, , 

a Scorpii, (Antares,).. , 

» Draconis, 

a. Trianguli Australia, 



e Ursse Minoris, 
a. Heeculis, . . . . 

<r Octantis, 

Deaconis, . . . . 



* Ophiuchi, 

y Deaconis, 

/u l Sagittarii, 

$ Ues^e Minoris, . 

« Lye^s, (Vega,). 

Lye^e, 

£ Aquil^e, 

S Aquil^e, 



y Aquil^e, 

* Aquil,e, (Altair,). 

8> Aquil.e, 

* 2 Capri corni, 



« 8 Right Afcen, 



2 

1 .2 
3 

3. 

3.3 
2 
5 
1 

2.3 

2 .3 
1 

2.3 

3 
1 
1 

1 

3 
3 
3 



2 

2.3 
4 
2 

3 

1 
3 
2 



3.4 



2 

2 

3.4 



1 

3 

3 

3 A 

3 

1 .2 
3.4 

3 



10 39 6.223 

10 54 10.737 

11 5 54.583 
1 11 38.718 

11 41 12.066 

11 45 42.219 

12 9 26.893 
12 18 4.916 

12 26 18.465 

12 48 49 007 

13 17 5.233 
13 41 27.894 

13 47 21.140 

13 53 0.800 

14 8 38.366 
14 29 11.925 

14 38 15.706 
14 42 22.132 

14 51 13.199 

15 8 43.595 

15 28 10.083 

15 36 41.077 

15 49 41.194 

15 56 29.397 

16 6 16.830 
16 19 58.461 
16 21 55.119 
16 32 25.090 



Annual Yar 



2.3051 
3.8001 
3.1928 
3.0010 

4- 3.0654* 
3.1874 
3.3409 
3.2710 

-f- 3.1342 

2.8403 
3.1512 
2.3525* 

4- 2.8606 
4.1508 
2.7336* 
4.0165* 

+ 2.6229 
-j- 3.3102 

— 0.2692 
+ 3.2226 

+ 2.5279 
4- 2.9391 

— 2.3520 
+ 3.4742 

+ 3.1382 
3.6638 
0.7960 

4- 6.2587 



17 1 55.988 — 6.5328*11 
17 7 37.617 4- 2.7320 
17 22 55.004 106.8627 
17 26 57.473 1.3513 



17 27 47.219 

17 53 1.955 

18 4 33.276 
18 22 0.703 

18 31 43.3P6 
18 44 23.696 

18 58 19.965 

19 17 43.889 

19 38 56.278 
19 43 16128 

19 47 44.866 

20 9 30.316 



4- 2.7727 

1.3900 

4- 3.5861 

—19.2683: 

4- 2.0118 
2.2124 
2.7566 

4- 3.0086 

4- 2.8511 

2.9254* 

2.9440 

3.3315 



Declination. 



de». min. sec. 

S. 58 52 34.26 

JST.62 34 51.81 

N.21 21 59.86 

8.13 56 46.85 

N.15 25 58.12 
N 54 33 3.18 
S.78 27 26.15 
S.62 14 39.74 

S. 22 32 39.93 
N.39 9 4.18 
S. 10 21 20.80 
N.50 5 1.45 

N.19 10 21.03 

5.59 37 33.93 
N.19 59 12.07 

5.60 11 37.00 

N.27 43 35.23 
S. 15 23 53.52 

N.74 47 5.58 
S. 8 48 38.53 

N.27 14 11.07 
N. 6 54 49.88 
N.78 15 55.43 
S. 19 22 44.18 

S. 3 17 35.67 
S.26 5 4.58 
N.61 51 50.58 
S. 68 44 4.75 



82 16 52.30 
JSU4 34 12.6 
S.89 16 10.25 
N.52 25 3.28 



N.12 40 37.11 
N.51 30 33.50 
S. 21 5 36.14 
N.86 35 42.58 

N.38 38 35.33 
N.33 11 14.80 
N.13 38 20.49 
N. 2 48 43.64 

N.10 14 31.50 
N. 8 27 54.32 
N. 6 1 33.90 
S. 13 1 4.19 



Ann. Var. 



-18.33 
19.24 
19.50 
19.61 

—1999 
20.02 
20.04 
19.99 

—19.92 
19.60 
18.94 
18.12 

—17.89 
17.67 
18.94* 
15.12« 

—15.46 
15.23 
14.71 
13.63 

—12.33 
11.74 
10.80 
10.29 

— 9.55 

8.48 
8.32 
7.48 

— 5.03 

4.54 
3.14 

2.88 

— 2.81 

— 0.61 
4- 0.40 
4- 1.91 



+ 


2.77 




3.86 




5.05 


+ 


6 r 67 


4- 


8.39 




8.74 




8.55' 




10 74 



TABLES. 



Star's Name. 



a Pavonis, 

y Ursa Minoris, 

a CYGNI, 

6HCYGNI, 



Cygni, . 
a Cephei, 
/S Aquarii, 
/2 Cephei,. 



i Pegasi,.. 
a Aquarii, 
« Grais,.. . 
£" Pegasi, . 



a Pis. A.us.( Fomalhaut), 1 

* Pegasi (Markab), 2 

t Piscium, [4 .5 

y Cephei, 



o 

1 

5.i 

3 
3 
3 
3 

2.3 
3 
2 
3 



20 13 25.814 + 4.8046 

20 16 31.309!— 52.1273 

20 36 11.005+ 2.0418 

6320 59 59.947 2.6908* 



* 



Right Ascen, 



Annual Var 



21 

21 14 53.940 
21 23 26.875 
21 26 39.120 



6 23.073 -f- 2.5486 
1.4163 
3.1628 
0.8059 



21 36 37.346 

21 57 52.326 

21 58 29.837 

22 33 46.976 

22 49 7.531 

22 57 5.584 

23 32 1.736 
23 33 4.581 



+ 2.9441 
3.0831 
3.8134 

2.9837 

+ 3.3095 
2.9776 
3.0569 

4- 2.4042 



Declination. 



deg. mia. sec. 

S.57 13 19.50 
N.88 50 53.54 
N.44 43 57.43 
N.37 59 42.08 

N.29 35 53.03 
K61 56 4.55 
S. 6 14 44.46 
X.69 53 7.21 

N. 9 10 17.35 
S. 1 3 56.72 
S. 47 42 12.42 
N.10 1 44.67 



S.30 26 12.28+ 19.11 



Ann. Var. 



11.03 
11.22 
12.64 
17.48* 

14.57 
15.07 
15.56 
15.73 

16.26 
17.28 
17.30 
18.65 



NU4 22 40.12 
N. 4 47 30.74 
N.76 46 22.01 



19.31 
19.36* 
+ 19.92 



Those Annual Variations which includes proper motion are distinguished 
by an Asterisk. 



SUN'S RIGHT ASCENSION FOR 1846. 



Day 














of 

Mo. 


January. 


February. 


March. 


April. 


May. 


June. 


h. min. sec. 


h. min. sec. 


h. min. sec 


h. min. sec 


h. min. sec. 


h. min. sec. 


1 


18 46 52 


20 59 11 


22 48 17 


41 52 


2 23 6 


4 35 48 


5 


19 4 30 


21 15 22 


23 3 12 


56 26 


2 48 25 


4 52 12 


10 


19 26 21 


21 35 18 


23 21 40 


1 14 43 


3 7 47 


5 12 50 


15 


19 47 57 


21 54 54 


23 40 


1 33 6 


3 27 24 


5 33 34 


20 


20 9 17 


22 14 12 


23 58 14 


1 51 38 


3 47 15 


5 54 22 


25 


20 30 19 


22 33 14 


i 16 25 


2 10 22 


4 7 20 


6 15 10 


30 


20 51 




| 34 36 


2 29 17 


4 27 8 


6 35 55 


Day 

of 
Mo. 


July. 


August. 


September. 


October. 


November. 


December. 


b. mic. sec. 




h. mlo. sec. 


b. mi . .-tc. 


h min. sec. 


h. min. sec. 


1 


6 40 4 


8 44 55 


10 41 


12 29 4 


14 25 16 


16 29 1 


5 


6 56 34 


9 23 


10 55 29 


12 43 36 


14 41 2 


16 46 23 


10 


7 17 5 


9 19 29 


11 13 30 


13 1 54 


15 1 5 


17 8 17 


15 


7 37 25 


9 38 21 


11 31 28 


13 20 24 


15 21 28 


17 30 22 


20 


7 57 33 


9 56 60 


11 49 25 


13 39 8 


15 42 14 


17 52 33 


25 


8 17 28 


10 15 27 


12 7 24 


13 58 9 


16 3 19 


18 14 46 


30 


8 37 7 


10 33 44 


12 25 27 


14 17 27 


16 24 43 


18 36 57 



The R. A. in this table will answer for corresponding days, in other years, 
within four minutes ; and for periods of four years, the difference is only about 
seven seconds for each period. 



TABLE III. 



TABULAR VIEW OF TILE SOLAR SYSTEM. 



1 




Mean distance Mean dist.; 


Log. of 


Time of revolu- 


Log. of 


Names. 


miles. 


from the Sun the Earth's 


mean 


tions round 


times of 




in miles. dist. unity. 


distance. 


Sun. 


revolution 


Sua 


883000 








DAYS. 




Mercury . 


3224 


37 million 


0.387098 9.587818 


87.969258 


1.944324 


Venus . . . 


7687 


68 " 


0.723332 9.859306 


224.700787 


2.351610 


TheEarth 


7912 


95 " 


1.000000 


0.000000 


365.256383 


2562598 


Mars .... 


4189 


144 " 


1.523692 


0.182810 


686.979646 


2.836942 


Vesta . . . 


238 


224,340,000 2.36120 


0.373100 1324.289 


3.121991 


Iris 1 . 


1 


226 miilion 


2.37880 


0.3763841 1327.973 


3.123190 


Hebe 1 


> Unknown. 


230 " 


2.42190 


384004! 1375. nearly 


3.138303 


Flora [ * 


240 « 


2.52630 


0.402487 


1469.76 


3.167300 


AstreaJ . 


J 


246 " 


2.5895 


0.413211 


1512. nearly 


3.179547 


Juno 


1420 


253,600,000 


2.66514 


0.425710 


1594.721 * 


3.202700 


Ceres. .. . 


Not well (160 
known. }120 


263,236,000 


2.76910 


0.442334 


1683.064 


3.226086 


Pallas . . . 


265 million 


2.77125 


0.442725 


1685.162 


3.226610' 


Jupiter.. . 


89170 


490 " 


5.202776 


0.716212 4332.584821 


3.636738 


Saturn . . . 


79040 


900 " 


9.538786 


97947610759.219817 


4.03171S 


Uranus . . 


35000 


1800 « 


19.18239011 .282853,30686.8208 


4.486953 


Neptune . 


35000 


2850 " 


29.59 11.477121,60128.14 


4.779076] 



TABLE III. 

ELEMENTS OF ORBITS FOR THE EPOCH OP 1850, JANUARY 1, MEAN NOON A* 

GREENWICH. 





Inclinati'n 


Variation 


Long. of the 


Variation 


Longitude 


Variation 


Mean longi- 


Planets. 


of orbits 


in 100 


ascending 


in 100 


of 


in 100 


tude at 




to ecliptic. 


years. 


nodes. 


years. 


Perihelion. 


years. 


epoch. 


Mercury 


O ' " 

7 18 


+18.2 


O ' " 

46 34 40 


' 


O ' " 
75 9 47 


+ 93 


C 
327 17 9 


Venus. . 


3 23 26 


— 4.6 


75 17 40 


+51 


129 22 53 


+ 78 


243 58 4 


Earth... 










100 22 10 


103 


100 47 1 


Mars . . . 


1 51 6 


— 0.2 


48 20 24 


+42 


333 17 57 


+110 


182 9 30 


Vesta.. . 


7 8 29 


—12. 


103 20 47 


+26 


254 4 34 


157 


113 28 12 


Juno 


13 2 53 




170 53 




54 18 32 




165 17 38 


Ceres. . . 


10 37 17 




80 47 56 




147 25 41 




1 3 10 


Pallas . . 


34 37 44 




172 42 38 




121 30 13 





327 31 24 


Jupiter.. 


1 18 42 


—22. 


98 55 19 


+57 


1] 56 


+ 95 


160 21 50 


Saturn. . 


2 29 29 


—15. 


112 22 54 


+51 


90 7 


+116 


13 58 13 


Uranus. . 


46 27 


3. 


73 12 


+24 


168 14 47 


+ 87 


28 20 22 



* We give the logarithms in the tables, that the data may be at hand to exercise 
the student on Kepler's third law. 



TABLE III. 

TABULAR TIEW OF THE SOLAR SYSTEM. 



Names. 


Mass. 


Density. 


Gravity. 


Siderial. 
Rotation, 


Light and 
Heat. 


Mercury . . 


zsifisTTy 


3.244 


1.22 


h. m. s. 

24 5 28 


6.680 


Venus .... 


SotVtT 


0.994 


0.96 


23 21 7 


1.911 


Earth 


35?Wd' 


1.000 


1.00 


24 


1.000 


Mars 


ZFS&3S7 


0.973 


0.50 


24 39 21 


.431 


Jupiter . . . 


TffisT 


0.232 


2.70 


9 55 50 


.037 


Saturn 


ssfrff-? 


0.132 


1.25 


10 29 17 


.011 


Uranus . . . 


Tfilf 


0.246 


1.06 


Unknown. 


.003 


Sun 

[Moon 


1 


0.256 


28.19 


25d. I2h. 0m. 




WZJliVTtJS 


0.665 


0.18 


27 7 43 





TABLE III. 





Planets. 


Eccentricities 
of orbits. 


Variation in 100 
years. 


Motion in mean 

long, in 1 year 

of 365 days. 


Mean Daily 
Motion in 
longitude. 


Mercury . . . 

Venus 

Earth 

Mars 

Vesta 

Juno 

Ceres 

Pallas 

Jupiter 

Saturn 

Uranus 


0.20551494 
0.00686074 
0.01678357 
0.09330700 
0.08856000 
0.25556000 
0.07673780 
0.24199800 
0.04816210 
0.05615050 
0.04661080 


-|- .000003868 

— .000062711 

— .000041630 
+ .000090176 
-h .000004009 


O ' " 

53 43 3.6 
224 47 29.7 
—0 14 19.5 
191 17 9.1 


' " 

4 5 32 6 

1 36 7 8 
59 8.3 
31 26.7 
16 17.9 
13 33.7 
12 49.4 
12 48.7 
4 59.3 
2 0.6 
42.4 




— .000005830 






+ .000159350 

— .000312402 

— .000025072 


30 20 31.9 

12 13 36.1 

4 17 45.1 



TABLE III. 

LUNAR PERIODS. 

a. 

Mean sidereal revolution, 27.321661418 

Mean synodical revolution, 29.530588715 

Mean revolution of nodes (retrograde),. . . '. 6793.391080 

Mean revolution of perigee (direct), . ... 3232.575343 

Mean inclination of orbit, 5° 8' 48" 

Mean distance, in measure, of the equatorial radius of 

the earth, 29 SI 

Mean distance, in measure, of the mean radius, . . 30.2000Q 



TABLES. 



SATELLITES OF JUPITER. 



Sat. 


Mean Distance. 


Sidereal Revolu- 
tion. 


Inclination of 

Orbit to that of 

Jupiter. 


Mass ; that of 

Jupiter being 

1000000000. 


1 
2 
3 
4 


6 04853 

9.62347 

15.35024 

26.99835 


d. b. m. 

1 18 28 

3 13 14 

7 3 43 

16 16 32 


o 

3 5 30 

Variable. 
Variable. 
2 58 48 


17328 
23235 
88497 
42659 



SATELLITES OF SATURN. 



Sat. 


Mean 


Sidereal Revolu- 


Distance. 


tion. 






d. b. m. 


1 


33.51 


22 38 


2 


4.300 


1 8 53 


3 


5.284 


1 21 18 


4 


6.819 


2 17 45 


5 


9.524 


4 12 25 


6 


22.081 


15 22 41 


7 


64.359 


79 55 



Eccentricities and Inclinations. 



The orbits of the six inte- 
rior satellites are nearly cir- 
cular, and very nearly in the 
plane of the ring. That, of 
the seventh is considerably 
inclined to the rest, and ap- 
proaches nearer to coincidence 
with the ecliptic. 



SATELLITES OF URANUS. 



Sat. 


Mean 
Distance. 


Sidereal Period. 


Inclination to Ecliptic. 








Their orbits are inclined 


1? 


13.120 


5 21 25 


about 78° 58' to the ecliptic, 


2 


17.022 


8 16 56 5 


and their motion is retrograde. 


3? 


19.845 


10 »23 4 


The periods of the 2d and 4th 


4 


22.752 


13 11 8 59 


require a trifling correction. 


52 


45.507 


38 1 48 


The orbits appear to be nearly 


6? 


91.0Q8 


107 16 40 


circles. 



